Difference between revisions of "De Moivre's Theorem"

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(Extension of Euler's formula: clean up & uniformity)
(Extension of Euler's formula: Spelling/Grammar Check, typos fixed: Therefore → Therefore,)
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:<math>\left( e^{ix} \right)^n = e^{inx} \,</math>
 
:<math>\left( e^{ix} \right)^n = e^{inx} \,</math>
  
Therefore from [[Euler's formula]]:
+
Therefore, from [[Euler's formula]]:
  
 
:<math>e^{i(nx)} = \cos(nx) + i\sin(nx)\,</math>
 
:<math>e^{i(nx)} = \cos(nx) + i\sin(nx)\,</math>
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]

Revision as of 10:23, 15 July 2016

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: