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PrecalculusSuperchallengePolar Coordinates and Complex Numbers

Polar Coordinates and Complex Numbers · Superchallenge problem

Given that z+1z=1z+\dfrac1z=1, evaluate z2027+1z2027z^{2027}+\dfrac{1}{z^{2027}}. (Hint: z+z−1=2cos⁡θz+z^{-1}=2\cos\theta.)