C library - cacosh() function

---

---

The C complex library cacosh() function is used to calculate the complex arc hyperbolic cosine, i.e. inverse hyperbolic cosine of z with branch cut at value less than 1 along with real axis. This means that the function is continuous and single-valued everywhere except along the real axis where z<1.

The inverse hyperbolic cosine (acosh) z is defined as:
acosh(z)=ln(z + √(z2 - 1))

This function is depends on the type of z. If the z is the "float" type, we use cacoshf() to compute acosh, For long double type, use cacoshl(), and for double type, use cacosh().

Syntax

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

double complex cacosh( double complex z );

Parameters

This function accepts a single parameter −

• Z − It represent a complex number for which we want to calculate acosh.

Return Value

This function returns the complex inverse hyperbolic cosine of z in the interval [0; ∞) along the real axis and in the interval [−iπ +iπ] along the imaginary axis.

Example 1

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

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

int main() {
   double complex z = 2.0 + 3.0 * I;

   // Calculate the hyperbolic cosine
   double complex res = cacosh(z);
   printf("Inverse hyperbolic cosine: %.2f%+.2fi\n", creal(res), cimag(res));

   return 0;
}

Output

Following is the output −

Inverse hyperbolic cosine: 1.98+1.00i

Example 2

Let's see another example, calculate the inverse hyperbolic cosine of real axis using cacosh() function.

#include <stdio.h>
#include <math.h>
#include <complex.h>
 
int main(void)
{
    // inverse cosine of real axis
    double complex z = 1;
    double complex res = cacosh(z);
    printf("acosh(1+0i) = %f+%fi \n", creal(res), cimag(res));
}

Output

Following is the output −

acosh(1+0i) = 0.000000+0.000000i 

Example 3

The below C program, calculates the complex arc hyperbolic cosine after computing the conjugate of a complex number.

#include <stdio.h>
#include <complex.h>
#include <math.h>
int main() {
   double complex z = 1.0 + 2.0 * I;
   
   // Calculate the conjugate of z
   double complex conjugate = conj(z);

   // Compute the acosh of the conjugate
   double complex result = acosh(conjugate);

   // Display the result
   printf("Conjugate of z: %.2f + %.2fi\n", creal(conjugate), cimag(conjugate));
   printf("acosh(conjugate): %.2f + %.2fi\n", creal(result), cimag(result));

   return 0;
}

Output

Following is the output −

Conjugate of z: 1.00 + -2.00i
acosh(conjugate): 0.00 + 0.00i