sqrt
Calculates the square root of a complex number.
template<class Type>
complex<Type> sqrt(
const complex<Type>& _ComplexNum
);
Parameters
- _ComplexNum
The complex number whose square root is to be found.
Return Value
The square root of a complex number.
Remarks
The square root will have a phase angle in the half-open interval (-pi/2, pi/2].
The branch cuts in the complex plane are along the negative real axis.
The square root of a complex number will have a modulus that is the square root of the input number and an argument that is one-half that of the input number.
Example
// 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.
Requirements
Header: <complex>
Namespace: std