sqrt() function for complex number in C++

The complex version of sqrt() function is defined in the complex header file. This function is used to calculate the square root of the complex number z with a branch cut along the negative real axis.

Syntax:

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

Parameters: This method takes a mandatory parameter z which represents the complex number whose square root is to be calculated.

Return Value: This function returns the square root of the complex number z.

Below program illustrate the sqrt() function for complex number in C++:

cpp

// C++ program to demonstrate
// example of sqrt() function.

#include <complex>
#include <iostream>
#include <math.h>

using namespace std;

int main()
{
    cout << "Square root of -9 is ";
    cout << sqrt(complex<double>(-9.0, 0.0)) << endl;

    cout << "Square root of (-9, -0) is ";
    cout << sqrt(complex<double>(-9.0, -0.0)) << endl;

    return 0;
}

Output

Square root of -9 is (0,3)
Square root of (-9, -0) is (0,-3)

Time Complexity: O(√(a²+b²)) where a and b are the real and imaginary part of complex number.
Auxiliary Space: O(1)