Complex Numbers Spaced Around The Unit Circle

Algebra Level 4

Let \( z = \dfrac{\sqrt{2 + \sqrt{3}}}{2} + i \cdot \dfrac{\sqrt{2 - \sqrt{3}}}{2}\). Find \(\displaystyle \sum_{k=0}^{2016} z^k\).

Clarification: \(i = \sqrt{-1}\).

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