: Mathématiques: Euler's formula

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Euler's formula

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 $x$ :
${\\displaystyle e^{ix}=\\cos x+i\\sin x,}$
where $e$ is the base of the natural logarithm, $i$ is the imaginary unit, and $cos$ and $sin$ are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted $cis x$ ("cosine plus i sine"). The formula is still valid if $x$ is a complex number, and so some authors refer to the more general complex version as Euler's formula.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Euler%27s_formula)

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