Difference between revisions of "De Moivre's Theorem"

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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...)
 
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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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'''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>
 
:<math>\left(\cos x+i\sin x\right)^n=\cos\left(nx\right)+i\sin\left(nx\right)\,</math>

Revision as of 15:22, 6 March 2008

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: