sqrt

2015-07-29

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

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