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 can follow these steps:

### Step 1: Express \( a + ib \) in terms of \( x \)
We start with the equation:
\[ a + ib = \frac{(x+i)^2}{2x^2 + 1} \]
Calculating \( (x+i)^2 \):
...