I should note that this theorem was proven by de Moivre by induction on n, before the reign of Euler.
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De Moivre's Theorem 
My first experience went something like:
"Wait why on earth is that tru--. Oh right.. Euler..again.."pic.twitter.com/VRXsMS2bRB
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I always think of the UCNs (unit complex numbers), or the circle group [https://en.wikipedia.org/wiki/Circle_group …], which are in Feynman's "path integral" formulation of QM.
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The log.
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