If `a + i b =((x+i)^2)/(2x^2+1),`prove that `a^2+b^2=((x^2+1)^2)/((2x^2+1)^2)`

Explanation

To prove that \( a^2 + b^2 = \frac{(x^2 + 1)^2}{(2x^2 + 1)^2} \) given that \( a + ib = \frac{(x + i)^2}{2x^2 + 1} \), we will follow these steps:

### Step 1: Express \( a + ib \) in terms of \( x \)
Given:
\[ a + ib = \frac{(x + i)^2}{2x^2 + 1} \]
We can expand \( (x + i)^2 \):
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