NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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
<< Previous page TOC INDEX Next page >>
De Moivre's Theorem
As a more complicated example of the value of the polar form, we'll proveDe 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.
