# 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 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:

 `// 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)
```

Example 2:

 `// 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)
```

Example 3:

 `// 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)
```

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