# Complex Polygon

**Algebra**Level 4

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**

**Note:**

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

\(i\) is the imaginary unit |