C library - clog() function

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The C complex library clog() function is used to calculate the complex natural (base-e) logarithm of z (complex number) with branch cut along the negative real axis.

This function is depends on the type of z(complex number). If the z is of the "float" type, we can use clogf() to compute complex logarithm, For type long double, use clogl(), and for type double, use clog().

Note: The natural logarithm of a complex number z can be represented using its polar coordinates (r,θ), where r is the magnitude (or modulus) of the z and θ is the argument (or phase angle). The natural logarithm ln(z) in terms of these polar coordinates is given by: ln(z)=ln(r)+i(θ+2nπ)

Syntax

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

double complex clog( double complex z )

Parameters

This function accepts a single parameter −

• Z − It represent a complex number for which we want to compute natural logarithm.

Return Value

This function returns, the complex natural logarithm of z (complex number), in the range of a strip in the interval [−iπ, +iπ] along the imaginary axis and mathematically unbounded along the real axis.

Example 1

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

#include <stdio.h>
#include <complex.h>

int main() {
   double complex z = 3.0 + 4.0*I; 
   
   // Compute ln(z)
   double complex result = clog(z);
   printf("clog(%f + %fi) = %f + %fi\n", creal(z), cimag(z), creal(result), cimag(result));
   return 0;
}

Output

Following is the output −

clog(3.000000 + 4.000000i) = 1.609438 + 0.927295i

Example 2

Calculate natural log with -ve real part.

Let's see another example, we use clog() to calculate the natural (base-e) logarithm.

#include <stdio.h>
#include <complex.h>

int main() {
   double complex z = -3.0 + 4.0*I; 
   
   // Compute ln(z)
   double complex result = clog(z);
   printf("clog(%f + %fi) = %f + %fi\n", creal(z), cimag(z), creal(result), cimag(result));
   return 0;
}

Output

Following is the output −

clog(-3.000000 + 4.000000i) = 1.609438 + 2.214297i

Example 3

Calculate natural logarithm with -ve real and -ve imag

Now, lets calculate the natural (base-e) logarithm of (-3.0 + -4.0*I)

#include <stdio.h>
#include <complex.h>

int main() {
   double complex z = -3.0 + -4.0*I; 
   
   // Compute ln(z)
   double complex result = clog(z);
   printf("clog(%f + %fi) = %f + %fi\n", creal(z), cimag(z), creal(result), cimag(result));
   return 0;
}

Output

Following is the output −

clog(-3.000000 + -4.000000i) = 1.609438 + -2.214297i