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Line 1: − '''De Moivre’s Theorem''' is a fundamental statement of [[complex analysis]], where ''i'' represents the square root of (-1): − :<math>\left(\cos x+i\sin x\right)^n=\cos\left(nx\right)+i\sin\left(nx\right)\,</math> − − ==Extension of [[Euler's formula]]== − De Moivre's formula is a trivial extension of [[Euler's formula]]: − − :<math>e^{ix} = \cos x + i\sin x\,</math> − − Because − − :<math>\left( e^{ix} \right)^n = e^{inx} \,</math> − − Therefore from [[Euler's formula]]: − − :<math>e^{i(nx)} = \cos(nx) + i\sin(nx)\,</math> − [[category:mathematics]]
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