C library - cacos() function

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The C complex library cacos() function perform the task of complex arcsine or inverse cosine of a given complex number. This function is defined under the header <complex.h> and it is available since C99.

Syntax

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

double complex cacos(double complex z);

Parameters

This function accept only a single parameter −

• z: It is a complex number which we want to operate the arcsine.

Return Value

The function returns the complex arcsine value(z), when no error occurs.

Example 1

Following is the C library program that shows the usage of cacos() function.

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

int main() {
   double complex z = 1.0 + 2.0 * I; 
   double complex result = cacos(z);
   printf("cacos(%lf + %lfi) = %lf + %lfi\n", creal(z), cimag(z), creal(result), cimag(result));
   return 0;
}

Output

On execution of above code, we get the following result −

cacos(1.000000 + 2.000000i) = 1.143718 + -1.528571i

Example 2

Below the program implement the series formula term = -(z * z) * (2 * i - 1) / (2 * i) using loop iterators within the recursive function.

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

double complex cacos_sol(double complex z, int n) {
   double complex sum = z;
   double complex term = z;

   for (int i = 1; i <= n; ++i) {
      term *= -(z * z) * (2 * i - 1) / (2 * i);
      sum += term;
   }

   return sum;
}

int main() {
   double complex z = 1.0 + 2.0 * I; 
   int terms = 10; 
   double complex result = cacos_sol(z, terms);
   printf("cacos(%lf + %lfi) = %lf + %lfi (approximated with %d terms)\n", creal(z), cimag(z), creal(result), cimag(result), terms);
   return 0;
}

Output

After executing the above code, we get the following result −

cacos(1.000000 + 2.000000i) = -522414.418148 + -4291552.656029i (approximated with 10 terms)

Example 3

The custom function cacos_recursive() accepts two parameters which is z and n to calculate the number of terms. When the n^th terms reaches to 0, the function returns the result value as z(complex number).

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

double complex cacos_recursive(double complex z, int n) {
   if (n == 0) {
       return z;
   }
   double complex term = -(z * z) * (2 * n - 1) / (2 * n) * cacos_recursive(z, n - 1);
   return term;
}

int main() {

   double complex z = 1.0 + 2.0 * I; 
   int terms = 10; 
   double complex result = cacos_recursive(z, terms);
   printf("cacos(%lf + %lfi) = %lf + %lfi (approximated with %d terms)\n", creal(z), cimag(z), creal(result), cimag(result), terms);
   return 0;
}

Output

The above code produces the following result −

cacos(1.000000 + 2.000000i) = -522414.418148 + -4291552.656029i (approximated with 10 terms)