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New page: 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\le...
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]]
:<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]]