C library - cproj() function

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The C complex library cproj() function is used to calculate the projection of z (complex number) on the Riemann sphere. Projection refers to a mapping or transformation that takes a point or a set of points from one space and maps them onto another space.

In mathematics, the Riemann sphere is a model for the complex plane. It maps all points on the plane to points on the sphere, introducing infinity as a representation of the behaviour of a complex function at infinity.

Syntax

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

double complex cproj( double complex z );

Parameters

This function accepts a single parameter −

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

Return Value

This function returns a complex value that may be type such as double, float, or long double, which represents the projection of z on the Riemann sphere.

Example 1

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

#include <stdio.h>
#include <complex.h>
#include <math.h> 
int main()
{
   double complex proj1 = cproj(1 + 2*I);
   printf("cproj(1+2i) = %.1f%+.1fi\n", creal(proj1),cimag(proj1));
   
   double complex proj2 = cproj(INFINITY+2.0*I);
   printf("cproj(Inf+2i) = %.1f%+.1fi\n", creal(proj2),cimag(proj2));
}

Output

Following is the output −

cproj(1+2i) = 1.0+2.0i
cproj(Inf+2i) = inf+0.0i

Example 2

Let's see another example, we create a complex number using the CMPLX(). We then use cproj() to calculate the projection of complex number.

#include <stdio.h>
#include <complex.h>
#include <math.h>
int main()
{
   double real = 3;
   double imag = 4;
   double complex z  = CMPLX(real, imag);
   
   double proj = cproj(z);
   
   printf("Complex number: %.1f + %.1fi\n", creal(z), cimag(z));    
   
   printf("Projection of complex number = %.1f + %.1fi\n", creal(proj),cimag(proj));
}

Output

Following is the output −

Complex number: 3.0 + 4.0i
Projection of complex number = 3.0 + 0.0i

Example 3

The below c example, calculate the projection of the negative complex number.

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

int main(void) {
   double complex z = -3.0 + -4.0*I;

   // find the project of complex number
   double proj = cproj(z);

   printf("Complex number: %.2f + %.2fi\n", creal(z), cimag(z));
   printf("project of complex number: %.2f + %.2fi", creal(proj), creal(proj));
   return 0;
}

Output

Following is the output −

Complex number: -3.00 + -4.00i
project of complex number: -3.00 + -3.00i