# proj() function for Complex Numbers in C++

• Difficulty Level : Expert
• Last Updated : 17 Aug, 2022

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 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 ` `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 ` `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 ` `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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