De Moivre's Theorem

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). De Moivre's Theorem

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De Moivre’s Theorem

As a more complicated example of the value of the polar form, we’ll proveDe Moivre’s theorem:

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Working this out using sum-of-angle identities from trigonometry is laborious. However, using Euler’s identity, De Moivre’s theorem simply “falls out”:
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Moreover, by the power of the method used to show the result,$n$ can be any real number, not just an integer.

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