MathLiveEuler's formula
Relates the complex exponential to cosine and sine, showing that e raised to an imaginary multiple of x traces a point on the unit circle. It is used throughout complex analysis, trigonometry, and electrical engineering to convert between exponential and trigonometric forms.
e^{ix} = \cos x + i \sin xWhat the symbols mean
| Euler's number, the base of the natural logarithm (approximately 2.71828) | |
| the imaginary unit, satisfying i^2 = -1 | |
| a real number, usually an angle in radians | |
| cosine of x | |
| sine of x |
About this formula
- FieldMathematics
- TopicComplex analysis
- LevelUniversity
- Also calledEuler formula complex exponential, complex exponential trigonometric identity, Euler's identity, exponential form of complex number, cos x plus i sin x
- SourceWikidata Q184871
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