Complex Numbers Spaced Around The Unit Circle

Algebra Level 3

Let z=2+32+i232 z = \dfrac{\sqrt{2 + \sqrt{3}}}{2} + i \cdot \dfrac{\sqrt{2 - \sqrt{3}}}{2}. Find k=02016zk\displaystyle \sum_{k=0}^{2016} z^k.

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

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