polar

Article
07/11/2012

Returns the complex number, which corresponds to a specified modulus and argument, in Cartesian form.

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

Parameters

_Modulus
The modulus of the complex number being input.
_Argument
The argument of the complex number being input.

Return Value

Cartesian form of the complex number specified in polar form.

Remarks

The polar form of a complex number provides the modulus r and the argument , where these parameters are related to the real and imaginary Cartesian components a and b by the equations a = r * cos ( ) and b = r * sin ().

Example

// 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.

Requirements

Header: <complex>

Namespace: std

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