proj() function for Complex Numbers in C++

The proj() function is a built-in function and is defined in the complex header file. This function is used to find the projection of complex number z onto the Riemann sphere.

Syntax:

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

Parameter:



  • z: This method takes a mandaory parameter z which represents the complex number.

Return value: This function returns the projection of complex number z onto the Riemann sphere.

Below programs illustrate the proj() function in C++:

Example 1:

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// C++ program to demonstrate
// example of proj() function
  
#include <bits/stdc++.h>
using namespace std;
  
int main()
{
    // defines the complex number: (2 + 2i)
    complex<double> complexnumber(2, 2);
  
    cout << "proj" << complexnumber << " = " 
                   << proj(complexnumber) << endl;
  
    return 0;
}

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Output:

proj(2,2) = (2,2)

Example 2:

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// C++ program to demonstrate
// example of proj() function.
  
#include <bits/stdc++.h>
using namespace std;
  
int main()
{
    complex<double> complexnumber(INFINITY, -2);
  
    cout << "proj" << complexnumber << " = " 
                   << proj(complexnumber) << endl;
  
    return 0;
}

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Output:

proj(inf,-2) = (inf,-0)

Example 3:

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// C++ program to demonstrate
// example of proj() function.
  
#include <bits/stdc++.h>
using namespace std;
  
int main()
{
    complex<double> complexnumber(2, -INFINITY);
  
    cout << "proj" << complexnumber << " = " 
                   << proj(complexnumber) << endl;
  
    return 0;
}

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Output:

proj(2,-inf) = (inf,-0)


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