Euler's formula

mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function

AI overview

Euler's formula is a mathematical equation that shows how complex exponential functions are fundamentally connected to the familiar trigonometric functions (like sine and cosine). This relationship is considered foundational in complex analysis because it reveals deep connections between different areas of mathematics that initially seem unrelated.

AI-generated from the Wikipedia summary — may contain errors.

Wikidata facts

Instance of: theorem
Named after: Leonhard Euler
Image: Euler's formula.svg

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time of discovery or invention: 1748-00-00
discoverer or inventor: Leonhard Euler
Commons category: Euler's formula
on focus list of Wikimedia project: Wikipedia:Vital articles/Level/4
maintained by WikiProject: WikiProject Mathematics
studied by: trigonometry

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Encyclopedic overview

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has

Excerpted from Wikipedia’s “Euler's formula” article, available under the CC BY-SA 4.0 licence.

Euler's formula

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