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−  '''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>
 
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−  ==Extension of [[Euler's formula]]==
 
−  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>
 
−  [[category:mathematics]]
 