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