C in a Nutshell

Name

cexp

Synopsis

Calculates the natural exponential of a complex number

#include <complex.h>
double complexcexp( double complex z );
float complex cexpf( float complex z );
long double complex cexpl( long double complex z );

The return value of the cexp() function is e raised to the power of the function’s argument, or e^z, where e is Euler’s number, 2.718281.... Furthermore, in complex mathematics, e^zi = cos(z) + sin(z) × i for any complex number z.

Tip

The natural exponential function cexp() is the inverse of the natural logarithm, clog().

Example

// Demonstrate Euler's theorem in the form
// e^(I*z) = cos(z) + I * sin(z)

double complex z = 2.2 + 3.3 * I;
double complex c, d;

c =cexp( z * I );
d = ccos( z ) + csin( z ) * I ;

printf( "cexp( z*I ) yields %.2f %+.2f \xD7 I.\n",
        creal(c), cimag(c) );
printf( "ccos( z ) + csin( z ) * I yields %.2f %+.2f \xD7 I.\n",
        creal(d), cimag(d) );

This code produces the following output:

cexp( z*I ) yields -0.02 +0.03 × I.
ccos( z ) + csin( z ) * I yields -0.02 +0.03 × I.

See Also

ccos(), csin(), clog(), cpow(), csqrt()