Find the multiplicative inverse of the following complex number: `(2+sqrt(3)i)^2`

Explanation

To find the multiplicative inverse of the complex number \((2 + \sqrt{3}i)^2\), we will follow these steps:

### Step 1: Simplify the Complex Number
We start by simplifying \((2 + \sqrt{3}i)^2\) using the formula for the square of a binomial, \((a + b)^2 = a^2 + 2ab + b^2\).

Let \(a = 2\) and \(b = \sqrt{3}i\):
\[
(2 + \sqrt{3}i)^2 = 2^2 + 2 \cdot 2 \cdot \sqrt{3}i + (\sqrt{3}i)^2
...