**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW
VERSION:** "Mathematics of the Discrete
Fourier Transform (DFT), with Audio Applications --- Second
Edition", by Julius
O. Smith III, W3K
Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright ©
*2017-09-28* by Julius O. Smith III -
Center for Computer Research
in Music and Acoustics (CCRMA), Stanford University

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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.