Square root of two Complex Numbers

Given two positive integers A and B representing the complex number Z in the form of Z = A + i * B, the task is to find the square root of the given complex number.

Examples:

Input: A = 0, B =1
Output:
The Square roots are: 
0.707107 + 0.707107*i
-0.707107 - 0.707107*i

Input: A = 4, B = 0
Output:
The Square roots are: 
2
-2

Approach: The given problem can be solved based on the following observations:

• It is known that the square root of a complex number is also a complex number.
• Then considering the square root of the complex number equal to X + i*Y, the value of (A + i*B) can be expressed as:
  • A + i * B = (X + i * Y) * (X + i * Y)
  • A + i * B = X² - Y²+ 2 * i * X * Y
• Equating the value of real and complex parts individually:

From the above observations, calculate the value of X and Y using the above formula and print the value (X + i*Y) as the resultant square root value of the given complex number.

Below is the implementation of the above approach:

The Square roots are: 
0.707107+0.707107*i
-0.707107-0.707107*i

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