MathLiveDe Moivre's formula
It gives the nth power of a complex number written in polar form as a cosine plus i times sine, for any integer n, by multiplying the angle by n. It is used for computing powers and roots of complex numbers and deriving trigonometric identities.
\left(\cos \theta + \mathrm{i} \sin \theta\right)^n = \cos (n\theta) + \mathrm{i} \sin (n\theta)What the symbols mean
| angle (in radians) | |
| integer exponent | |
| imaginary unit, satisfying \mathrm{i}^2 = -1 |
About this formula
- FieldMathematics
- TopicComplex numbers
- LevelUniversity
- Also calledde Moivre's theorem, de Moivre's identity, de Moivre theorem complex numbers, powers of complex numbers in polar form, nth power of cos plus i sin, complex number power trigonometric form
- SourceWikidata Q190556
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