De Moivre's Theorem

Rarely Tested

For integer $$n$$, $$\left( \cos \theta + i \sin \theta \right)^n = \cos (n\theta) + i \sin (n\theta)$$.

Also holds for $$z^n = |z|^n \left( \cos (n\theta) + i \sin (n\theta) \right)$$.

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