On the complex plane, a regular polygon formed by connecting each consecutive point that is a solution to the equation $x^n = 1,$ is centered at the origin and has a vertex at $z = \bigg(\frac{\sqrt{3}}{2} + \frac{i}{2}\bigg).$
Let **A** be the minimum possible number of sides found on this polygon, and let **B** be area of the polygon with **A** sides.
Find the value of **A** $+$ **B**

You may use a calculator to evaluate the area of the polygon | |

$i$ is the imaginary unit |