If `x - i y =sqrt((a-i b)/(c-i d))` prove that `x^2+y^2=(a^2+b^2)/(c^2+d^2)`

Explanation

To prove that \( x^2 + y^2 = \frac{a^2 + b^2}{c^2 + d^2} \) given that \( x - iy = \sqrt{\frac{a - ib}{c - id}} \), we can follow these steps:

### Step 1: Multiply both sides by \( x + iy \)
We start with the equation:
\[ x - iy = \sqrt{\frac{a - ib}{c - id}} \]
Now, we multiply both sides by \( x + iy \):
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