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):
 
  
:<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]]
 

Revision as of 16:18, 6 March 2009