Difference between revisions of "De Moivre's Theorem"

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:<math>e^{i(nx)} = \cos(nx) + i\sin(nx)\,</math>
 
:<math>e^{i(nx)} = \cos(nx) + i\sin(nx)\,</math>
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Revision as of 02:28, 13 July 2016

De Moivre’s Theorem is a fundamental statement of complex analysis, where i represents the square root of (-1):

Extension of Euler's formula

De Moivre's formula is a trivial extension of Euler's formula:

Because

Therefore from Euler's formula: