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proj() function for Complex Numbers in C++

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  • Difficulty Level : Expert
  • Last Updated : 17 Aug, 2022
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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 mandatory 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++ are as follows: 

Example 1:
 

CPP




// 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;
}

Output: 

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

 

Time Complexity: O(1)
Auxiliary Space: O(1)

Example 2:

CPP




// 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;
}

Output: 

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

 

Time Complexity: O(1)
Auxiliary Space: O(1)

Example 3: 

CPP




// 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;
}

Output: 

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

 

Time Complexity: O(1)
Auxiliary Space: O(1)


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