exp
Returns the exponential function of a complex number.
template<class Type>
complex<Type> exp(
const complex<Type>& _ComplexNum
);
Parameters
- _ComplexNum
The complex number whose exponential is being determined.
Return Value
The complex number that is the exponential of the input complex number.
Example
// 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;
}
Output
Complex number c1 = (1,0.523599)
Complex number c2 = exp ( c1 ) = (2.3541,1.35914)
The modulus of c2 is: 2.71828
The argument of c2 is: 0.523599 radians, which is 30 degrees.
The complex components exp (vci), where abs (vci) = 1
& arg (vci) = i * pi / 3 of the vector v1 are:
(-1,2.06823e-013)
with argument = 180 degrees
modulus = 1
(-0.5,-0.866025)
with argument = -120 degrees
modulus = 1
(1,0)
with argument = 0 degrees
modulus = 1
(0.5,0.866025)
with argument = 60 degrees
modulus = 1
(-0.5,0.866025)
with argument = 120 degrees
modulus = 1
(-1,-2.06823e-013)
with argument = -180 degrees
modulus = 1
Requirements
Header: <complex>
Namespace: std