# 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 09:35, 22 June 2010

**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: