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


You may use a calculator to evaluate the area of the polygon
\(i\) is the imaginary unit

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