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

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DavidB4-bot (Talk | contribs) (→Extension of Euler's formula: Spelling/Grammar Check, typos fixed: Therefore → Therefore,) |
(Don't need to define "i"--it's fundamental. It's primordial. The fact that it's one of the square roots of -1 (and -i is the other) is a theorem.) |
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− | '''De Moivre’s Theorem''' is a fundamental statement of [[complex analysis]] | + | '''De Moivre’s Theorem''' is a fundamental statement of [[complex analysis]]: |

:<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> |

## Latest revision as of 18:56, 14 July 2018

**De Moivre’s Theorem** is a fundamental statement of complex analysis:

## Extension of Euler's formula

De Moivre's formula is a trivial extension of Euler's formula:

Because

Therefore, from Euler's formula: