Difference between revisions of "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):
  
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:<math>\left(\cos x+i\sin x\right)^n=\cos\left(nx\right)+i\sin\left(nx\right)\,</math>
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==Extension of [[Euler's formula]]==
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De Moivre's formula is a trivial extension of [[Euler's formula]]:
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:<math>e^{ix} = \cos x + i\sin x\,</math>
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Because
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:<math>\left( e^{ix} \right)^n = e^{inx} \,</math>
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Therefore from [[Euler's formula]]:
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:<math>e^{i(nx)} = \cos(nx) + i\sin(nx)\,</math>
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[[category:mathematics]]

Revision as of 16:21, 6 March 2009

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: