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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 ().

// 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.