# 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): | + | '''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: