# Difference between revisions of "De Moivre's Theorem"

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DavidB4-bot (Talk | contribs) (→Extension of Euler's formula: clean up & uniformity) |
DavidB4-bot (Talk | contribs) (→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: