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Showing content from https://cplusplus.com/reference/complex/proj/ below:

function template

std::proj complex (1)

template<class T> complex<T> proj (const complex<T>& x);

complex (1)

template<class T> complex<T> proj (const complex<T>& x);

arithmetic type (2)

complex<double> conj (ArithmeticType x);

Complex projection.

Returns the projection of the complex number x onto the Riemann sphere.

The projection of x is x, except for complex infinities, which are mapped to the complex value with a real component of INFINITY and an imaginary component of 0.0 or -0.0 (where supported), depending on the sign of the imaginary component of x.

Additional overloads are provided for arguments of any fundamental arithmetic type: In this case, the function assumes the value has a zero imaginary component.

The return type is complex<double>, except if the argument is float or long double (in which case, the return type is the complex instantiation for that type: either complex<float> or complex<long double>).

Parameters

x: Complex value.

Return value Complex projection of x onto the Riemann sphere.

Example

// proj example
#include <iostream>     // std::cout
#include <complex>      // std::complex, std::proj
#include <limits>       // std::numeric_limits

int main ()
{
  std::complex<double> mycomplex (std::numeric_limits<double>::infinity(),2.0);

  std::cout << "The projection of " << mycomplex << " is " << std::proj(mycomplex) << '\n';

  return 0;
}

Possible output (representation of infinities may vary):

The projection of (inf,2) is (inf,0)