`<complex>` – funkce

Abs

Vypočítá moduly komplexního čísla.

template <class Type>
Type abs(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož modul je třeba určit.

Návratová hodnota

Moduly komplexního čísla.

Poznámky

Moduly komplexního čísla jsou měřítkem délky vektoru představujícího komplexní číslo. Moduly komplexního čísla a + bi je druhou odmocninou (a² + b2), napsané |a + bi|. Normou komplexního čísla a + bi je (² + b^2). Normou komplexního čísla je čtverec jeho modulu.

Příklad

// complex_abs.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // Complex numbers can be entered in polar form with
   // modulus and argument parameter inputs but are
   // stored in Cartesian form as real & imag coordinates
   complex <double> c1 ( polar ( 5.0 ) );   // Default argument = 0
   complex <double> c2 ( polar ( 5.0 , pi / 6 ) );
   complex <double> c3 ( polar ( 5.0 , 13 * pi / 6 ) );
   cout << "c1 = polar ( 5.0 ) = " << c1 << endl;
   cout << "c2 = polar ( 5.0 , pi / 6 ) = " << c2 << endl;
   cout << "c3 = polar ( 5.0 , 13 * pi / 6 ) = " << c3 << endl;

   // The modulus and argument of a complex number can be recovered
   // using abs & arg member functions
   double absc1 = abs ( c1 );
   double argc1 = arg ( c1 );
   cout << "The modulus of c1 is recovered from c1 using: abs ( c1 ) = "
        << absc1 << endl;
   cout << "Argument of c1 is recovered from c1 using:\n arg ( c1 ) = "
        << argc1 << " radians, which is " << argc1 * 180 / pi
        << " degrees." << endl;

   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is recovered from c2 using: abs ( c2 ) = "
        << absc2 << endl;
   cout << "Argument of c2 is recovered from c2 using:\n arg ( c2 ) = "
        << argc2 << " radians, which is " << argc2 * 180 / pi
        << " degrees." << endl;

   // Testing if the principal angles of c2 and c3 are the same
   if ( (arg ( c2 ) <= ( arg ( c3 ) + .00000001) ) ||
        (arg ( c2 ) >= ( arg ( c3 ) - .00000001) ) )
      cout << "The complex numbers c2 & c3 have the "
           << "same principal arguments."<< endl;
   else
      cout << "The complex numbers c2 & c3 don't have the "
           << "same principal arguments." << endl;
}

c1 = polar ( 5.0 ) = (5,0)
c2 = polar ( 5.0 , pi / 6 ) = (4.33013,2.5)
c3 = polar ( 5.0 , 13 * pi / 6 ) = (4.33013,2.5)
The modulus of c1 is recovered from c1 using: abs ( c1 ) = 5
Argument of c1 is recovered from c1 using:
arg ( c1 ) = 0 radians, which is 0 degrees.
The modulus of c2 is recovered from c2 using: abs ( c2 ) = 5
Argument of c2 is recovered from c2 using:
arg ( c2 ) = 0.523599 radians, which is 30 degrees.
The complex numbers c2 & c3 have the same principal arguments.

acos

template<class T> complex<T> acos(const complex<T>&);

acosh

template<class T> complex<T> acosh(const complex<T>&);

Arg

Extrahuje argument ze komplexního čísla.

template <class Type>
Type arg(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož argument má být určen.

Návratová hodnota

Argument komplexního čísla.

Poznámky

Argument je úhel, který komplexní vektor vytvoří s kladnou skutečnou osou v komplexní rovině. U komplexního čísla a + BI se argument rovná arkustan(b/a). Úhel má pozitivní smysl při měření směru proti směru hodinových ručiček z kladné reálné osy a záporného smyslu při měření ve směru hodinových ručiček. Hlavní hodnoty jsou větší než -pí a menší než nebo rovno +pí.

Příklad

// complex_arg.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // Complex numbers can be entered in polar form with
   // modulus and argument parameter inputs but are
   // stored in Cartesian form as real & imag coordinates
   complex <double> c1 ( polar ( 5.0 ) );   // Default argument = 0
   complex <double> c2 ( polar ( 5.0 , pi / 6 ) );
   complex <double> c3 ( polar ( 5.0 , 13 * pi / 6 ) );
   cout << "c1 = polar ( 5.0 ) = " << c1 << endl;
   cout << "c2 = polar ( 5.0 , pi / 6 ) = " << c2 << endl;
   cout << "c3 = polar ( 5.0 , 13 * pi / 6 ) = " << c3 << endl;

   // The modulus and argument of a complex number can be rcovered
   // using abs & arg member functions
   double absc1 = abs ( c1 );
   double argc1 = arg ( c1 );
   cout << "The modulus of c1 is recovered from c1 using: abs ( c1 ) = "
        << absc1 << endl;
   cout << "Argument of c1 is recovered from c1 using:\n arg ( c1 ) = "
        << argc1 << " radians, which is " << argc1 * 180 / pi
        << " degrees." << endl;

   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is recovered from c2 using: abs ( c2 ) = "
        << absc2 << endl;
   cout << "Argument of c2 is recovered from c2 using:\n arg ( c2 ) = "
        << argc2 << " radians, which is " << argc2 * 180 / pi
        << " degrees." << endl;

   // Testing if the principal angles of c2 and c3 are the same
   if ( (arg ( c2 ) <= ( arg ( c3 ) + .00000001) ) ||
        (arg ( c2 ) >= ( arg ( c3 ) - .00000001) ) )
      cout << "The complex numbers c2 & c3 have the "
           << "same principal arguments."<< endl;
   else
      cout << "The complex numbers c2 & c3 don't have the "
           << "same principal arguments." << endl;
}

c1 = polar ( 5.0 ) = (5,0)
c2 = polar ( 5.0 , pi / 6 ) = (4.33013,2.5)
c3 = polar ( 5.0 , 13 * pi / 6 ) = (4.33013,2.5)
The modulus of c1 is recovered from c1 using: abs ( c1 ) = 5
Argument of c1 is recovered from c1 using:
arg ( c1 ) = 0 radians, which is 0 degrees.
The modulus of c2 is recovered from c2 using: abs ( c2 ) = 5
Argument of c2 is recovered from c2 using:
arg ( c2 ) = 0.523599 radians, which is 30 degrees.
The complex numbers c2 & c3 have the same principal arguments.

asin

template<class T> complex<T> asin(const complex<T>&);

asinh

template<class T> complex<T> asinh(const complex<T>&);

atan

template<class T> complex<T> atan(const complex<T>&);

atanh

template<class T> complex<T> atanh(const complex<T>&);

conj

Vrátí komplexní konjugování komplexního čísla.

template <class Type>
complex<Type> conj(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož komplexní konjugování je vráceno.

Návratová hodnota

Komplexní konjugování vstupního komplexního čísla.

Poznámky

Komplexní konjugování komplexního čísla a + bi je - bi. Součin komplexního čísla a jeho konjugace je normou čísla a2 + b2.

Příklad

// complex_conj.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;

   complex <double> c1 ( 4.0 , 3.0 );
   cout << "The complex number c1 = " << c1 << endl;

   double dr1 = real ( c1 );
   cout << "The real part of c1 is real ( c1 ) = "
        << dr1 << "." << endl;

   double di1 = imag ( c1 );
   cout << "The imaginary part of c1 is imag ( c1 ) = "
        << di1 << "." << endl;

   complex <double> c2 = conj ( c1 );
   cout << "The complex conjugate of c1 is c2 = conj ( c1 )= "
        << c2 << endl;

   double dr2 = real ( c2 );
   cout << "The real part of c2 is real ( c2 ) = "
        << dr2 << "." << endl;

   double di2 = imag ( c2 );
   cout << "The imaginary part of c2 is imag ( c2 ) = "
        << di2 << "." << endl;

   // The real part of the product of a complex number
   // and its conjugate is the norm of the number
   complex <double> c3 = c1 * c2;
   cout << "The norm of (c1 * conj (c1) ) is c1 * c2 = "
        << real( c3 ) << endl;
}

The complex number c1 = (4,3)
The real part of c1 is real ( c1 ) = 4.
The imaginary part of c1 is imag ( c1 ) = 3.
The complex conjugate of c1 is c2 = conj ( c1 )= (4,-3)
The real part of c2 is real ( c2 ) = 4.
The imaginary part of c2 is imag ( c2 ) = -3.
The norm of (c1 * conj (c1) ) is c1 * c2 = 25

cos

Vrátí kosinus komplexního čísla.

template <class Type>
complex<Type> cos(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož kosinus je určen.

Návratová hodnota

Komplexní číslo, které je kosinus vstupního komplexního čísla.

Poznámky

Identity definující komplexní kosinusy:

cos (z) = (1/2)*(exp (iz) + exp (- iz) )

cos (z) = cos (a + bi) = cos (a) cosh ( b) - isin (a) sinh (b)

Příklad

// complex_cos.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;
   complex <double> c1 ( 3.0 , 4.0 );
   cout << "Complex number c1 = " << c1 << endl;

   // Values of cosine of a complex number c1
   complex <double> c2 = cos ( c1 );
   cout << "Complex number c2 = cos ( c1 ) = " << c2 << endl;
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is: " << absc2 << endl;
   cout << "The argument of c2 is: "<< argc2 << " radians, which is "
        << argc2 * 180 / pi << " degrees." << endl << endl;

   // Cosines of the standard angles in the first
   // two quadrants of the complex plane
   vector <complex <double> > v1;
   vector <complex <double> >::iterator Iter1;
   complex <double> vc1  ( polar (1.0, pi / 6) );
   v1.push_back( cos ( vc1 ) );
   complex <double> vc2  ( polar (1.0, pi / 3) );
   v1.push_back( cos ( vc2 ) );
   complex <double> vc3  ( polar (1.0, pi / 2) );
   v1.push_back( cos ( vc3) );
   complex <double> vc4  ( polar (1.0, 2 * pi / 3) );
   v1.push_back( cos ( vc4 ) );
   complex <double> vc5  ( polar (1.0, 5 * pi / 6) );
   v1.push_back( cos ( vc5 ) );
   complex <double> vc6  ( polar (1.0,  pi ) );
   v1.push_back( cos ( vc6 ) );

   cout << "The complex components cos (vci), where abs (vci) = 1"
        << "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
   for ( Iter1 = v1.begin( ) ; Iter1 != v1.end( ) ; Iter1++ )
      cout << *Iter1 << endl;
}

Complex number c1 = (3,4)
Complex number c2 = cos ( c1 ) = (-27.0349,-3.85115)
The modulus of c2 is: 27.3079
The argument of c2 is: -3.00009 radians, which is -171.893 degrees.

The complex components cos (vci), where abs (vci) = 1
& arg (vci) = i * pi / 6 of the vector v1 are:
(0.730543,-0.39695)
(1.22777,-0.469075)
(1.54308,1.21529e-013)
(1.22777,0.469075)
(0.730543,0.39695)
(0.540302,-1.74036e-013)

obušek

Vrátí hyperbolický kosinus komplexního čísla.

template <class Type>
complex<Type> cosh(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož hyperbolický kosinus je určen.

Návratová hodnota

Komplexní číslo, které je hyperbolický kosinus vstupního komplexního čísla.

Poznámky

Identity definující komplexní hyperbolický kosinus:

cos (z) = (1/2)*( exp (z) + exp (- z) )

cos (z) = cosh (a + bi) = cosh (a) cos (b) + isinh (a) sin (b)

Příklad

// complex_cosh.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;
   complex <double> c1 ( 3.0 , 4.0 );
   cout << "Complex number c1 = " << c1 << endl;

   // Values of cosine of a complex number c1
   complex <double> c2 = cosh ( c1 );
   cout << "Complex number c2 = cosh ( c1 ) = " << c2 << endl;
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is: " << absc2 << endl;
   cout << "The argument of c2 is: "<< argc2 << " radians, which is "
        << argc2 * 180 / pi << " degrees." << endl << endl;

   // Hyperbolic cosines of the standard angles
   // in the first two quadrants of the complex plane
   vector <complex <double> > v1;
   vector <complex <double> >::iterator Iter1;
   complex <double> vc1  ( polar (1.0, pi / 6) );
   v1.push_back( cosh ( vc1 ) );
   complex <double> vc2  ( polar (1.0, pi / 3) );
   v1.push_back( cosh ( vc2 ) );
   complex <double> vc3  ( polar (1.0, pi / 2) );
   v1.push_back( cosh ( vc3) );
   complex <double> vc4  ( polar (1.0, 2 * pi / 3) );
   v1.push_back( cosh ( vc4 ) );
   complex <double> vc5  ( polar (1.0, 5 * pi / 6) );
   v1.push_back( cosh ( vc5 ) );
   complex <double> vc6  ( polar (1.0,  pi ) );
   v1.push_back( cosh ( vc6 ) );

   cout << "The complex components cosh (vci), where abs (vci) = 1"
        << "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
   for ( Iter1 = v1.begin( ) ; Iter1 != v1.end( ) ; Iter1++ )
      cout << *Iter1 << endl;
}

Complex number c1 = (3,4)
Complex number c2 = cosh ( c1 ) = (-6.58066,-7.58155)
The modulus of c2 is: 10.0392
The argument of c2 is: -2.28564 radians, which is -130.957 degrees.

The complex components cosh (vci), where abs (vci) = 1
& arg (vci) = i * pi / 6 of the vector v1 are:
(1.22777,0.469075)
(0.730543,0.39695)
(0.540302,-8.70178e-014)
(0.730543,-0.39695)
(1.22777,-0.469075)
(1.54308,2.43059e-013)

exp

Vrátí exponenciální funkci komplexního čísla.

template <class Type>
complex<Type> exp(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož exponenciální hodnota je určena.

Návratová hodnota

Komplexní číslo, které je exponenciálním vstupním komplexním číslem.

Příklad

// complex_exp.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>

int main() {
   using namespace std;
   double pi = 3.14159265359;
   complex <double> c1 ( 1 , pi/6 );
   cout << "Complex number c1 = " << c1 << endl;

   // Value of exponential of a complex number c1:
   // note the argument of c2 is determined by the
   // imaginary part of c1 & the modulus by the real part
   complex <double> c2 = exp ( c1 );
   cout << "Complex number c2 = exp ( c1 ) = " << c2 << endl;
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is: " << absc2 << endl;
   cout << "The argument of c2 is: "<< argc2 << " radians, which is "
        << argc2 * 180 / pi << " degrees." << endl << endl;

   // Exponentials of the standard angles
   // in the first two quadrants of the complex plane
   vector <complex <double> > v1;
   vector <complex <double> >::iterator Iter1;
   complex <double> vc1  ( 0.0 , -pi );
   v1.push_back( exp ( vc1 ) );
   complex <double> vc2  ( 0.0, -2 * pi / 3 );
   v1.push_back( exp ( vc2 ) );
   complex <double> vc3  ( 0.0, 0.0 );
   v1.push_back( exp ( vc3 ) );
   complex <double> vc4  ( 0.0, pi / 3 );
   v1.push_back( exp ( vc4 ) );
   complex <double> vc5  ( 0.0 , 2 * pi / 3 );
   v1.push_back( exp ( vc5 ) );
   complex <double> vc6  ( 0.0, pi );
   v1.push_back( exp ( vc6 ) );

   cout << "The complex components exp (vci), where abs (vci) = 1"
        << "\n& arg (vci) = i * pi / 3 of the vector v1 are:\n" ;
   for ( Iter1 = v1.begin() ; Iter1 != v1.end() ; Iter1++ )
      cout <<  ( * Iter1 ) << "\n     with argument = "
           << ( 180/pi ) * arg ( *Iter1 )
           << " degrees\n     modulus = "
           << abs ( * Iter1 ) << endl;
}

imag

Extrahuje imaginární komponentu komplexního čísla.

template <class Type>
Type imag(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož reálnou částí se má extrahovat.

Návratová hodnota

Imaginární část komplexního čísla jako globální funkce.

Poznámky

Tuto funkci šablony nelze použít k úpravě skutečné části komplexního čísla. Pokud chcete změnit skutečnou část, musí být nové komplexní číslo přiřazeno hodnotě komponenty.

Příklad

// complexc_imag.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   complex <double> c1 ( 4.0 , 3.0 );
   cout << "The complex number c1 = " << c1 << endl;

   double dr1 = real ( c1 );
   cout << "The real part of c1 is real ( c1 ) = "
        << dr1 << "." << endl;

   double di1 = imag ( c1 );
   cout << "The imaginary part of c1 is imag ( c1 ) = "
        << di1 << "." << endl;
}

The complex number c1 = (4,3)
The real part of c1 is real ( c1 ) = 4.
The imaginary part of c1 is imag ( c1 ) = 3.

protokol

Vrátí přirozený logaritmus komplexního čísla.

template <class Type>
complex<Type> log(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož přirozený logaritmus je určen.

Návratová hodnota

Komplexní číslo, které je přirozeným logaritmem vstupního komplexního čísla.

Poznámky

Řezy větví jsou podél záporné reálné osy.

Příklad

// complex_log.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>

int main() {
   using namespace std;
   double pi = 3.14159265359;
   complex <double> c1 ( 3.0 , 4.0 );
   cout << "Complex number c1 = " << c1 << endl;

   // Values of log of a complex number c1
   complex <double> c2 = log ( c1 );
   cout << "Complex number c2 = log ( c1 ) = " << c2 << endl;
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is: " << absc2 << endl;
   cout << "The argument of c2 is: "<< argc2 << " radians, which is "
        << argc2 * 180 / pi << " degrees." << endl << endl;

   // log of the standard angles
   // in the first two quadrants of the complex plane
   vector <complex <double> > v1;
   vector <complex <double> >::iterator Iter1;
   complex <double> vc1  ( polar (1.0, pi / 6) );
   v1.push_back( log ( vc1 ) );
   complex <double> vc2  ( polar (1.0, pi / 3) );
   v1.push_back( log ( vc2 ) );
   complex <double> vc3  ( polar (1.0, pi / 2) );
   v1.push_back( log ( vc3) );
   complex <double> vc4  ( polar (1.0, 2 * pi / 3) );
   v1.push_back( log ( vc4 ) );
   complex <double> vc5  ( polar (1.0, 5 * pi / 6) );
   v1.push_back( log ( vc5 ) );
   complex <double> vc6  ( polar (1.0,  pi ) );
   v1.push_back( log ( vc6 ) );

   cout << "The complex components log (vci), where abs (vci) = 1 "
        << "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
   for ( Iter1 = v1.begin() ; Iter1 != v1.end() ; Iter1++ )
      cout << *Iter1 << " " << endl;
}

log10

Vrátí logaritmus komplexního čísla o základu 10.

template <class Type>
complex<Type> log10(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož základní logaritmus je 10.

Návratová hodnota

Komplexní číslo, které je základem 10 logaritmu vstupního komplexního čísla.

Poznámky

Řezy větví jsou podél záporné reálné osy.

Příklad

// complex_log10.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>

int main() {
   using namespace std;
   double pi = 3.14159265359;
   complex <double> c1 ( 3.0 , 4.0 );
   cout << "Complex number c1 = " << c1 << endl;

   // Values of log10 of a complex number c1
   complex <double> c2 = log10 ( c1 );
   cout << "Complex number c2 = log10 ( c1 ) = " << c2 << endl;
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is: " << absc2 << endl;
   cout << "The argument of c2 is: "<< argc2 << " radians, which is "
        << argc2 * 180 / pi << " degrees." << endl << endl;

   // log10 of the standard angles
   // in the first two quadrants of the complex plane
   vector <complex <double> > v1;
   vector <complex <double> >::iterator Iter1;
   complex <double> vc1  ( polar (1.0, pi / 6) );
   v1.push_back( log10 ( vc1 ) );
   complex <double> vc2  ( polar (1.0, pi / 3) );
   v1.push_back( log10 ( vc2 ) );
   complex <double> vc3  ( polar (1.0, pi / 2) );
   v1.push_back( log10 ( vc3) );
   complex <double> vc4  ( polar (1.0, 2 * pi / 3) );
   v1.push_back( log10 ( vc4 ) );
   complex <double> vc5  ( polar (1.0, 5 * pi / 6) );
   v1.push_back( log10 ( vc5 ) );
   complex <double> vc6  ( polar (1.0,  pi ) );
   v1.push_back( log10 ( vc6 ) );

   cout << "The complex components log10 (vci), where abs (vci) = 1"
        << "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
   for ( Iter1 = v1.begin( ) ; Iter1 != v1.end( ) ; Iter1++ )
      cout << *Iter1 << endl;
}

norm

Extrahuje normu komplexního čísla.

template <class Type>
Type norm(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož normu je třeba určit.

Návratová hodnota

Normou komplexního čísla.

Poznámky

Normou komplexního čísla a + bi je (² + b^2). Normou komplexního čísla je čtverec jeho modulu. Moduly komplexního čísla jsou měřítkem délky vektoru představujícího komplexní číslo. Moduly komplexního čísla a + bi je druhou odmocninou (a² + b2), napsané |a + bi|.

Příklad

// complex_norm.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // Complex numbers can be entered in polar form with
   // modulus and argument parameter inputs but are
   // stored in Cartesian form as real & imag coordinates
   complex <double> c1 ( polar ( 5.0 ) );   // Default argument = 0
   complex <double> c2 ( polar ( 5.0 , pi / 6 ) );
   complex <double> c3 ( polar ( 5.0 , 13 * pi / 6 ) );
   cout << "c1 = polar ( 5.0 ) = " << c1 << endl;
   cout << "c2 = polar ( 5.0 , pi / 6 ) = " << c2 << endl;
   cout << "c3 = polar ( 5.0 , 13 * pi / 6 ) = " << c3 << endl;

   if ( (arg ( c2 ) <= ( arg ( c3 ) + .00000001) ) ||
        (arg ( c2 ) >= ( arg ( c3 ) - .00000001) ) )
      cout << "The complex numbers c2 & c3 have the "
           << "same principal arguments."<< endl;
   else
      cout << "The complex numbers c2 & c3 don't have the "
           << "same principal arguments." << endl;

   // The modulus and argument of a complex number can be recovered
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is recovered from c2 using: abs ( c2 ) = "
        << absc2 << endl;
   cout << "Argument of c2 is recovered from c2 using:\n arg ( c2 ) = "
        << argc2 << " radians, which is " << argc2 * 180 / pi
        << " degrees." << endl;

   // The norm of a complex number is the square of its modulus
   double normc2 = norm ( c2 );
   double sqrtnormc2 = sqrt ( normc2 );
   cout << "The norm of c2 given by: norm ( c2 ) = " << normc2 << endl;
   cout << "The modulus of c2 is the square root of the norm: "
        << "sqrt ( normc2 ) = " << sqrtnormc2 << ".";
}

c1 = polar ( 5.0 ) = (5,0)
c2 = polar ( 5.0 , pi / 6 ) = (4.33013,2.5)
c3 = polar ( 5.0 , 13 * pi / 6 ) = (4.33013,2.5)
The complex numbers c2 & c3 have the same principal arguments.
The modulus of c2 is recovered from c2 using: abs ( c2 ) = 5
Argument of c2 is recovered from c2 using:
arg ( c2 ) = 0.523599 radians, which is 30 degrees.
The norm of c2 given by: norm ( c2 ) = 25
The modulus of c2 is the square root of the norm: sqrt ( normc2 ) = 5.

polární

Vrátí komplexní číslo, které odpovídá zadanému modulu a argumentu v kartézské podobě.

template <class Type>
complex<Type> polar(const Type& _Modulus, const Type& _Argument = 0);

Parametry

_Modul
Moduly komplexního čísla, které je vstupní.

_Argument
Argument komplexního čísla, který je vstupní.

Návratová hodnota

Kartézská forma komplexního čísla zadaného v polární podobě.

Poznámky

Polární forma komplexního čísla poskytuje moduly r a argument p, kde tyto parametry souvisejí se skutečnými a imaginárními kartézským komponentami a a b rovnicemi a = r * cos p a b = r * sin p.

Příklad

// complex_polar.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // Complex numbers can be entered in polar form with
   // modulus and argument parameter inputs but are
   // stored in Cartesian form as real & imag coordinates
   complex <double> c1 ( polar ( 5.0 ) );   // Default argument = 0
   complex <double> c2 ( polar ( 5.0 , pi / 6 ) );
   complex <double> c3 ( polar ( 5.0 , 13 * pi / 6 ) );
   cout << "c1 = polar ( 5.0 ) = " << c1 << endl;
   cout << "c2 = polar ( 5.0 , pi / 6 ) = " << c2 << endl;
   cout << "c3 = polar ( 5.0 , 13 * pi / 6 ) = " << c3 << endl;

   if ( (arg ( c2 ) <= ( arg ( c3 ) + .00000001) ) ||
        (arg ( c2 ) >= ( arg ( c3 ) - .00000001) ) )
      cout << "The complex numbers c2 & c3 have the "
           << "same principal arguments."<< endl;
   else
      cout << "The complex numbers c2 & c3 don't have the "
           << "same principal arguments." << endl;

   // the modulus and argument of a complex number can be rcovered
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is recovered from c2 using: abs ( c2 ) = "
        << absc2 << endl;
   cout << "Argument of c2 is recovered from c2 using:\n arg ( c2 ) = "
        << argc2 << " radians, which is " << argc2 * 180 / pi
        << " degrees." << endl;
}

c1 = polar ( 5.0 ) = (5,0)
c2 = polar ( 5.0 , pi / 6 ) = (4.33013,2.5)
c3 = polar ( 5.0 , 13 * pi / 6 ) = (4.33013,2.5)
The complex numbers c2 & c3 have the same principal arguments.
The modulus of c2 is recovered from c2 using: abs ( c2 ) = 5
Argument of c2 is recovered from c2 using:
arg ( c2 ) = 0.523599 radians, which is 30 degrees.

zajatec

Vyhodnotí komplexní číslo získané zvýšením základu, který je komplexním číslem na mocninu jiného komplexního čísla.

template <class Type>
complex<Type> pow(const complex<Type>& _Base, int _Power);

template <class Type>
complex<Type> pow(const complex<Type>& _Base, const Type& _Power);

template <class Type>
complex<Type> pow(const complex<Type>& _Base, const complex<Type>& _Power);

template <class Type>
complex<Type> pow(const Type& _Base, const complex<Type>& _Power);

Parametry

_Základna
Jedná se o komplexní číslo nebo číslo typu parametru pro komplexní číslo, které je základem, který má být vyvolán na mocninu členskou funkcí.

_Moc
Celé číslo nebo komplexní číslo nebo číslo, které je typu parametru pro komplexní číslo, které je mocninou, na kterou má být základ vyvolán členskou funkcí.

Návratová hodnota

Komplexní číslo získané zvýšením zadané základny na zadanou mocninu.

Poznámky

Funkce efektivně převedou oba operandy na návratový typ a pak vrátí převedený levý na mocninu doprava.

Řez větve je podél záporné reálné osy.

Příklad

// complex_pow.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // First member function
   // type complex<double> base & type integer power
   complex <double> cb1 ( 3 , 4);
   int cp1 = 2;
   complex <double> ce1 = pow ( cb1 ,cp1 );

   cout << "Complex number for base cb1 = " << cb1 << endl;
   cout << "Integer for power = " << cp1 << endl;
   cout << "Complex number returned from complex base and integer power:"
        << "\n ce1 = cb1 ^ cp1 = " << ce1 << endl;
   double absce1 = abs ( ce1 );
   double argce1 = arg ( ce1 );
   cout << "The modulus of ce1 is: " << absce1 << endl;
   cout << "The argument of ce1 is: "<< argce1 << " radians, which is "
        << argce1 * 180 / pi << " degrees." << endl << endl;

   // Second member function
   // type complex<double> base & type double power
   complex <double> cb2 ( 3 , 4 );
   double cp2 = pi;
   complex <double> ce2 = pow ( cb2 ,cp2 );

   cout << "Complex number for base cb2 = " << cb2 << endl;
   cout << "Type double for power cp2 = pi = " << cp2 << endl;
   cout << "Complex number returned from complex base and double power:"
        << "\n ce2 = cb2 ^ cp2 = " << ce2 << endl;
   double absce2 = abs ( ce2 );
   double argce2 = arg ( ce2 );
   cout << "The modulus of ce2 is: " << absce2 << endl;
   cout << "The argument of ce2 is: "<< argce2 << " radians, which is "
        << argce2 * 180 / pi << " degrees." << endl << endl;

   // Third member function
   // type complex<double> base & type complex<double> power
   complex <double> cb3 ( 3 , 4 );
   complex <double> cp3 ( -2 , 1 );
   complex <double> ce3 = pow ( cb3 ,cp3 );

   cout << "Complex number for base cb3 = " << cb3 << endl;
   cout << "Complex number for power cp3= " << cp3 << endl;
   cout << "Complex number returned from complex base and complex power:"
        << "\n ce3 = cb3 ^ cp3 = " << ce3 << endl;
   double absce3 = abs ( ce3 );
   double argce3 = arg ( ce3 );
   cout << "The modulus of ce3 is: " << absce3 << endl;
   cout << "The argument of ce3 is: "<< argce3 << " radians, which is "
        << argce3 * 180 / pi << " degrees." << endl << endl;

   // Fourth member function
   // type double base & type complex<double> power
   double cb4 = pi;
   complex <double> cp4 ( 2 , -1 );
   complex <double> ce4 = pow ( cb4 ,cp4 );

   cout << "Type double for base cb4 = pi = " << cb4 << endl;
   cout << "Complex number for power cp4 = " << cp4 << endl;
   cout << "Complex number returned from double base and complex power:"
        << "\n ce4 = cb4 ^ cp4 = " << ce4 << endl;
   double absce4 = abs ( ce4 );
   double argce4 = arg ( ce4 );
   cout << "The modulus of ce4 is: " << absce4 << endl;
   cout << "The argument of ce4 is: "<< argce4 << " radians, which is "
        << argce4 * 180 / pi << " degrees." << endl << endl;
}

Complex number for base cb1 = (3,4)
Integer for power = 2
Complex number returned from complex base and integer power:
ce1 = cb1 ^ cp1 = (-7,24)
The modulus of ce1 is: 25
The argument of ce1 is: 1.85459 radians, which is 106.26 degrees.

Complex number for base cb2 = (3,4)
Type double for power cp2 = pi = 3.14159
Complex number returned from complex base and double power:
ce2 = cb2 ^ cp2 = (-152.915,35.5475)
The modulus of ce2 is: 156.993
The argument of ce2 is: 2.91318 radians, which is 166.913 degrees.

Complex number for base cb3 = (3,4)
Complex number for power cp3= (-2,1)
Complex number returned from complex base and complex power:
ce3 = cb3 ^ cp3 = (0.0153517,-0.00384077)
The modulus of ce3 is: 0.0158249
The argument of ce3 is: -0.245153 radians, which is -14.0462 degrees.

Type double for base cb4 = pi = 3.14159
Complex number for power cp4 = (2,-1)
Complex number returned from double base and complex power:
ce4 = cb4 ^ cp4 = (4.07903,-8.98725)
The modulus of ce4 is: 9.8696
The argument of ce4 is: -1.14473 radians, which is -65.5882 degrees.

proj

template<class T> complex<T> proj(const complex<T>&);

real

Extrahuje skutečnou komponentu komplexního čísla.

template <class Type>
Type real(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož reálnou částí se má extrahovat.

Návratová hodnota

Skutečná část komplexního čísla jako globální funkce.

Poznámky

Tuto funkci šablony nelze použít k úpravě skutečné části komplexního čísla. Pokud chcete změnit skutečnou část, musí být nové komplexní číslo přiřazeno hodnotě komponenty.

Příklad

// complex_real.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   complex <double> c1 ( 4.0 , 3.0 );
   cout << "The complex number c1 = " << c1 << endl;

   double dr1 = real ( c1 );
   cout << "The real part of c1 is real ( c1 ) = "
        << dr1 << "." << endl;

   double di1 = imag ( c1 );
   cout << "The imaginary part of c1 is imag ( c1 ) = "
        << di1 << "." << endl;
}

The complex number c1 = (4,3)
The real part of c1 is real ( c1 ) = 4.
The imaginary part of c1 is imag ( c1 ) = 3.

sin

Vrátí sinus komplexního čísla.

template <class Type>
complex<Type> sin(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož sinus je určen.

Návratová hodnota

Komplexní číslo, které je sinusem vstupního komplexního čísla.

Poznámky

Identity definující komplexní sines:

sin (z) = (1/2 i)*( exp (iz) - exp (- iz) )

sin (z) = sin (a + bi) = sin (a) cosh (b) + icos (a) sinh (b)

Příklad

// complex_sin.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;
   complex <double> c1 ( 3.0 , 4.0 );
   cout << "Complex number c1 = " << c1 << endl;

   // Values of sine of a complex number c1
   complex <double> c2 = sin ( c1 );
   cout << "Complex number c2 = sin ( c1 ) = " << c2 << endl;
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is: " << absc2 << endl;
   cout << "The argument of c2 is: "<< argc2 << " radians, which is "
        << argc2 * 180 / pi << " degrees." << endl << endl;

   // sines of the standard angles in the first
   // two quadrants of the complex plane
   vector <complex <double> > v1;
   vector <complex <double> >::iterator Iter1;
   complex <double> vc1  ( polar ( 1.0, pi / 6 ) );
   v1.push_back( sin ( vc1 ) );
   complex <double> vc2  ( polar ( 1.0, pi / 3 ) );
   v1.push_back( sin ( vc2 ) );
   complex <double> vc3  ( polar ( 1.0, pi / 2 ) );
   v1.push_back( sin ( vc3 ) );
   complex <double> vc4  ( polar ( 1.0, 2 * pi / 3 ) );
   v1.push_back( sin ( vc4 ) );
   complex <double> vc5  ( polar ( 1.0, 5 * pi / 6 ) );
   v1.push_back( sin ( vc5 ) );
   complex <double> vc6  ( polar ( 1.0, pi ) );
   v1.push_back( sin ( vc6 ) );

   cout << "The complex components sin (vci), where abs (vci) = 1"
        << "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
   for ( Iter1 = v1.begin( ) ; Iter1 != v1.end( ) ; Iter1++ )
      cout << *Iter1 << endl;
}

Complex number c1 = (3,4)
Complex number c2 = sin ( c1 ) = (3.85374,-27.0168)
The modulus of c2 is: 27.2903
The argument of c2 is: -1.42911 radians, which is -81.882 degrees.

The complex components sin (vci), where abs (vci) = 1
& arg (vci) = i * pi / 6 of the vector v1 are:
(0.85898,0.337596)
(0.670731,0.858637)
(-1.59572e-013,1.1752)
(-0.670731,0.858637)
(-0.85898,0.337596)
(-0.841471,-1.11747e-013)

Sinh

Vrátí hyperbolický sinus komplexního čísla.

template <class Type>
complex<Type> sinh(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož hyperbolický sinus je určen.

Návratová hodnota

Komplexní číslo, které je hyperbolický sinus vstupního komplexního čísla.

Poznámky

Identity definující komplexní hyperbolické siny:

sinh (z) = (1/2)*( exp (z) - exp (- z) )

sinh (z) = sinh (a + bi) = sinh (a) cos (b) + icosh (a) sin (b)

Příklad

// complex_sinh.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;
   complex <double> c1 ( 3.0 , 4.0 );
   cout << "Complex number c1 = " << c1 << endl;

   // Values of sine of a complex number c1
   complex <double> c2 = sinh ( c1 );
   cout << "Complex number c2 = sinh ( c1 ) = " << c2 << endl;
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is: " << absc2 << endl;
   cout << "The argument of c2 is: "<< argc2 << " radians, which is "
        << argc2 * 180 / pi << " degrees." << endl << endl;

   // Hyperbolic sines of the standard angles in
   // the first two quadrants of the complex plane
   vector <complex <double> > v1;
   vector <complex <double> >::iterator Iter1;
   complex <double> vc1  ( polar ( 1.0, pi / 6 ) );
   v1.push_back( sinh ( vc1 ) );
   complex <double> vc2  ( polar ( 1.0, pi / 3 ) );
   v1.push_back( sinh ( vc2 ) );
   complex <double> vc3  ( polar ( 1.0, pi / 2 ) );
   v1.push_back( sinh ( vc3) );
   complex <double> vc4  ( polar ( 1.0, 2 * pi / 3 ) );
   v1.push_back( sinh ( vc4 ) );
   complex <double> vc5  ( polar ( 1.0, 5 * pi / 6 ) );
   v1.push_back( sinh ( vc5 ) );
   complex <double> vc6  ( polar ( 1.0, pi ) );
   v1.push_back( sinh ( vc6 ) );

   cout << "The complex components sinh (vci), where abs (vci) = 1"
        << "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
   for ( Iter1 = v1.begin( ) ; Iter1 != v1.end( ) ; Iter1++ )
      cout << *Iter1 << endl;
}

Complex number c1 = (3,4)
Complex number c2 = sinh ( c1 ) = (-6.54812,-7.61923)
The modulus of c2 is: 10.0464
The argument of c2 is: -2.28073 radians, which is -130.676 degrees.

The complex components sinh (vci), where abs (vci) = 1
& arg (vci) = i * pi / 6 of the vector v1 are:
(0.858637,0.670731)
(0.337596,0.85898)
(-5.58735e-014,0.841471)
(-0.337596,0.85898)
(-0.858637,0.670731)
(-1.1752,-3.19145e-013)

Sqrt

Vypočítá druhou odmocninu komplexního čísla.

template <class Type>
complex<Type> sqrt(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož druhou odmocninu se má najít.

Návratová hodnota

Druhá odmocnina komplexního čísla.

Poznámky

Druhá odmocnina bude mít v polootevřené intervalu fázi (-pí/2, pí/2].

Větve řezy v komplexní rovině jsou podél záporné reálné osy.

Druhá odmocnina komplexního čísla bude mít moduly, které jsou druhou odmocninou vstupního čísla a argumentem, který představuje polovinu vstupního čísla.

Příklad

// complex_sqrt.cpp
// compile with: /EHsc
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;

   // Complex numbers can be entered in polar form with
   // modulus and argument parameter inputs but are
   // stored in Cartesian form as real & imag coordinates
   complex <double> c1 ( polar ( 25.0 , pi / 2 ) );
   complex <double> c2 = sqrt ( c1 );
   cout << "c1 = polar ( 5.0 ) = " << c1 << endl;
   cout << "c2 = sqrt ( c1 ) = " << c2 << endl;

   // The modulus and argument of a complex number can be recovered
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is recovered from c2 using: abs ( c2 ) = "
        << absc2 << endl;
   cout << "Argument of c2 is recovered from c2 using:\n arg ( c2 ) = "
        << argc2 << " radians, which is " << argc2 * 180 / pi
        << " degrees." << endl;

   // The modulus and argument of c2 can be directly calculated
   absc2 = sqrt( abs ( c1 ) );
   argc2 = 0.5 * arg ( c1 );
   cout << "The modulus of c2 = sqrt( abs ( c1 ) ) =" << absc2 << endl;
   cout << "The argument of c2 = ( 1 / 2 ) * arg ( c1 ) ="
        << argc2 << " radians,\n which is " << argc2 * 180 / pi
        << " degrees." << endl;
}

c1 = polar ( 5.0 ) = (-2.58529e-012,25)
c2 = sqrt ( c1 ) = (3.53553,3.53553)
The modulus of c2 is recovered from c2 using: abs ( c2 ) = 5
Argument of c2 is recovered from c2 using:
arg ( c2 ) = 0.785398 radians, which is 45 degrees.
The modulus of c2 = sqrt( abs ( c1 ) ) =5
The argument of c2 = ( 1 / 2 ) * arg ( c1 ) =0.785398 radians,
which is 45 degrees.

opálení

Vrátí tangens komplexního čísla.

template <class Type>
complex<Type> tan(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož tangens je určen.

Návratová hodnota

Komplexní číslo, které je tangens vstupního komplexního čísla.

Poznámky

Identity definující komplexní kotangens:

tan (z) = sin (z) / cos (z) = ( exp (iz) - exp (- iz) ) / i( exp (iz) + exp (- iz) )

Příklad

// complex_tan.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;
   complex <double> c1 ( 3.0 , 4.0 );
   cout << "Complex number c1 = " << c1 << endl;

   // Values of cosine of a complex number c1
   complex <double> c2 = tan ( c1 );
   cout << "Complex number c2 = tan ( c1 ) = " << c2 << endl;
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is: " << absc2 << endl;
   cout << "The argument of c2 is: "<< argc2 << " radians, which is "
        << argc2 * 180 / pi << " degrees." << endl << endl;

   // Hyperbolic tangent of the standard angles
   // in the first two quadrants of the complex plane
   vector <complex <double> > v1;
   vector <complex <double> >::iterator Iter1;
   complex <double> vc1  ( polar ( 1.0, pi / 6 ) );
   v1.push_back( tan ( vc1 ) );
   complex <double> vc2  ( polar ( 1.0, pi / 3 ) );
   v1.push_back( tan ( vc2 ) );
   complex <double> vc3  ( polar ( 1.0, pi / 2 ) );
   v1.push_back( tan ( vc3) );
   complex <double> vc4  ( polar ( 1.0, 2 * pi / 3 ) );
   v1.push_back( tan ( vc4 ) );
   complex <double> vc5  ( polar ( 1.0, 5 * pi / 6 ) );
   v1.push_back( tan ( vc5 ) );
   complex <double> vc6  ( polar ( 1.0,  pi ) );
   v1.push_back( tan ( vc6 ) );

   cout << "The complex components tan (vci), where abs (vci) = 1"
        << "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
   for ( Iter1 = v1.begin() ; Iter1 != v1.end() ; Iter1++ )
      cout << *Iter1 << endl;
}

Complex number c1 = (3,4)
Complex number c2 = tan ( c1 ) = (-0.000187346,0.999356)
The modulus of c2 is: 0.999356
The argument of c2 is: 1.57098 radians, which is 90.0107 degrees.

The complex components tan (vci), where abs (vci) = 1
& arg (vci) = i * pi / 6 of the vector v1 are:
(0.713931,0.85004)
(0.24356,0.792403)
(-4.34302e-014,0.761594)
(-0.24356,0.792403)
(-0.713931,0.85004)
(-1.55741,-7.08476e-013)

tanh

Vrátí hyperbolický tangens komplexního čísla.

template <class Type>
complex<Type> tanh(const complex<Type>& complexNum);

Parametry

complexNum
Jedná se o komplexní číslo, jehož hyperbolický tangens je určen.

Návratová hodnota

Komplexní číslo, které je hyperbolický tangens vstupního komplexního čísla.

Poznámky

Identity definující komplexní hyperbolický kotangens:

tanh (z) = sinh (z) / cosh (z) = ( exp (z) - exp (- z) ) / ( exp (z) + exp (- z) )

Příklad

// complex_tanh.cpp
// compile with: /EHsc
#include <vector>
#include <complex>
#include <iostream>

int main( )
{
   using namespace std;
   double pi = 3.14159265359;
   complex <double> c1 ( 3.0 , 4.0 );
   cout << "Complex number c1 = " << c1 << endl;

   // Values of cosine of a complex number c1
   complex <double> c2 = tanh ( c1 );
   cout << "Complex number c2 = tanh ( c1 ) = " << c2 << endl;
   double absc2 = abs ( c2 );
   double argc2 = arg ( c2 );
   cout << "The modulus of c2 is: " << absc2 << endl;
   cout << "The argument of c2 is: "<< argc2 << " radians, which is "
        << argc2 * 180 / pi << " degrees." << endl << endl;

   // Hyperbolic tangents of the standard angles
   // in the first two quadrants of the complex plane
   vector <complex <double> > v1;
   vector <complex <double> >::iterator Iter1;
   complex <double> vc1  ( polar ( 1.0, pi / 6 ) );
   v1.push_back( tanh ( vc1 ) );
   complex <double> vc2  ( polar ( 1.0, pi / 3 ) );
   v1.push_back( tanh ( vc2 ) );
   complex <double> vc3  ( polar ( 1.0, pi / 2 ) );
   v1.push_back( tanh ( vc3 ) );
   complex <double> vc4  ( polar ( 1.0, 2 * pi / 3 ) );
   v1.push_back( tanh ( vc4 ) );
   complex <double> vc5  ( polar ( 1.0, 5 * pi / 6 ) );
   v1.push_back( tanh ( vc5 ) );
   complex <double> vc6  ( polar ( 1.0, pi ) );
   v1.push_back( tanh ( vc6 ) );

   cout << "The complex components tanh (vci), where abs (vci) = 1"
        << "\n& arg (vci) = i * pi / 6 of the vector v1 are:\n" ;
   for ( Iter1 = v1.begin( ) ; Iter1 != v1.end( ) ; Iter1++ )
      cout << *Iter1 << endl;
}

Complex number c1 = (3,4)
Complex number c2 = tanh ( c1 ) = (1.00071,0.00490826)
The modulus of c2 is: 1.00072
The argument of c2 is: 0.00490474 radians, which is 0.281021 degrees.

The complex components tanh (vci), where abs (vci) = 1
& arg (vci) = i * pi / 6 of the vector v1 are:
(0.792403,0.24356)
(0.85004,0.713931)
(-3.54238e-013,1.55741)
(-0.85004,0.713931)
(-0.792403,0.24356)
(-0.761594,-8.68604e-014)

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Last updated on 2025-11-07

Sdílet prostřednictvím

<complex> – funkce

Abs

Parametry

Návratová hodnota

Poznámky

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acos

acosh

Arg

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conj

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cos

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obušek

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exp

Parametry

Návratová hodnota

Příklad

imag

Parametry

Návratová hodnota

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protokol

Parametry

Návratová hodnota

Poznámky

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log10

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Návratová hodnota

Poznámky

Příklad

norm

Parametry

Návratová hodnota

Poznámky

Příklad

polární

Parametry

Návratová hodnota

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zajatec

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proj

real

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Návratová hodnota

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sin

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Návratová hodnota

Poznámky

Příklad

Sinh

Parametry

`<complex>` – funkce