Express the following in the standard form `a+i b :((1+i)^2)/(3-i)`

Explanation

To express the complex number \(\frac{(1+i)^2}{3-i}\) in the standard form \(a + ib\), we will follow these steps:

### Step 1: Expand the numerator
We start with the numerator \((1+i)^2\). Using the formula for the square of a binomial, \((a+b)^2 = a^2 + 2ab + b^2\), we have:

\[ (1+i)^2 = 1^2 + 2 \cdot 1 \cdot i + i^2 \]
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