C library - cexp() function

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The C complex library cexp() function is used to calculate the complex base-e exponential of the given z(complex number).

This function is depends on the type of z(complex number). If the z is of the "float" type, we can use cexpf() to compute complex base-e exponential, For type long double, use cexpl(), and for type double, use cexp().

Note: The complex exponential function e^z for z = a+bi equals e^a cis(b), where cis(b) is cos(b) + isin(b). The exponential function is an entire function in the complex plane and has no branch cuts.

Syntax

Following is the C library syntax of cexp() function −

double complex cexp( double complex z );

Parameters

This function accepts a single parameter −

• Z − It represent a complex number for which we want to compute the exponential.

Return Value

This function returns, e raised to the power of z (e^z) if no errors occur. where e represent the base of the natural logarithm.

Example 1

Following is the basic c program to demonstrate the use of cexp() of a complex number.

#include <stdio.h>
#include <complex.h>
#include <math.h>
int main()
{
   double complex z = 1 + 2*I;
   double expo = cexp(z);
   printf("z = %.1f + %.1fi\n", creal(z),cimag(z));
   printf("exponent of z = %.1f + %.1fi\n", creal(expo),cimag(expo));
}

Output

Following is the output −

z = 1.0 + 2.0i
exponent of z = -1.1 + 0.0i

Example 2

Calculate the value of e^iπ

Let's see another example, we use of Euler's formula to calculate the exponential of a complex number using the cexp() function.

#include <stdio.h>
#include <math.h>
#include <complex.h>
 
int main(void)
{
   double PI = acos(-1);
   double complex z = cexp(I * PI); // Euler's formula
   printf("exp(i*pi) = %.1f%+.1fi\n", creal(z), cimag(z)); 
}

Output

Following is the output −

exp(i*pi) = -1.0+0.0i

Example 3

Exponent of -ve complex number

The below c example, we calculate the e^{-3 + -4i} using the cexp() function.

#include <stdio.h>
#include <complex.h>
#include <math.h>
int main()
{
   double complex z = -3 + -4*I;
   double expo = cexp(z);
   printf("z = %.1f + %.1fi\n", creal(z),cimag(z));
   printf("exponent of z = %.1f + %.1fi\n", creal(expo),cimag(expo));
}

Output

Following is the output −

z = -3.0 + -4.0i
exponent of z = -0.0 + 0.0i