De Moivre's Theorem

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

\left(\cos x+i\sin x\right)^n=\cos\left(nx\right)+i\sin\left(nx\right)\,

Extension of Euler's formula

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

e^{ix} = \cos x + i\sin x\,

Because

\left( e^{ix} \right)^n = e^{inx} \,

Therefore from Euler's formula:

e^{i(nx)} = \cos(nx) + i\sin(nx)\,
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