Modulus of a Complex Number

Given a complex number z, the task is to determine the modulus of this complex number. Note: Given a complex number z = a + ib the modulus is denoted by |z| and is defined as [latex]\left | z \right | = \sqrt{a^{2}+b^{2}}[/latex] Examples:

Input: z = 3 + 4i 
Output: 5 |z| = (3² + 4²)^1/2 = (9 + 16)^1/2 = 5 

Input: z = 6 - 8i 
Output: 10 
Explanation: |z| = (6² + (-8)²)^1/2 = (36 + 64)^1/2 = 10

Approach: For the given complex number z = x + iy:

1. Find the real and imaginary parts, x and y respectively.

If z = x +iy

Real part = x
Imaginary part = y

1. Find the square of x and y separately.

Square of Real part = x2
Square of Imaginary part = y2

1. Find the sum of the computed squares.

Sum = Square of Real part 
 + Square of Imaginary part
 = x2 + y2

1. Find the square root of the computed sum. This will be the modulus of the given complex number

[latex]\left | z \right | = \sqrt{x^{2}+y^{2}}[/latex]

Below is the implementation of the above approach: 

5

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

As constant extra space is used