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 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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