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## De Moivre’s Theorem

As a more complicated example of the value of the polar form, we’ll prove

De Moivre’s theorem:

Working this out using sum-of-angle identities from trigonometry is laborious. However, using Euler’s identity, De Moivre’s theorem simply “falls out”:

Moreover, by the power of the method used to show the result, can be any real number, not just an integer.