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Display information for equation id:math.219374.0 on revision:219374

* Page found: Euler's formula (eq math.219374.0)

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Hash: 0ef933b93605a459e87fe63f3abf33af

TeX (original user input):

e^{ix} = \cos x + i\sin x \

TeX (checked):

e^{ix}=\cos x+i\sin x\

LaTeXML (experimental; uses MathML) rendering

MathML (3.401 KB / 735 B) :

e i x = cos x + i sin x superscript 𝑒 𝑖 𝑥 𝑥 𝑖 𝑥 {\displaystyle e^{{ix}}=\cos x+i\sin x\ }
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SVG (7.053 KB / 2.779 KB) :

e Superscript i times x Baseline equals cosine x plus i times sine x

MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools) rendering

MathML (0 B / 8 B) :

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SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: (e)^(i*x)= cos(x)+ i*sin(x)

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: cos($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos


\sin: Sine; Example: \sin@@{z}

Will be translated to: sin($0)

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin


I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Maple uses I for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \iunit


e: the mathematical constant e == Napier's constant == 2.71828182845... was translated to: e

exp(1): You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].

We keep it like it is! But you should know that Maple uses exp(1) for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \expe


i: the imaginary unit == the principal square root of -1 was translated to: i


Translation to Mathematica

In Mathematica: (e)^(i*x)= Cos[x]+ i*Sin[x]

Information about the conversion process:

\cos: Cosine; Example: \cos@@{z}

Will be translated to: Cos[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E2

Mathematica: https://reference.wolfram.com/language/ref/Cos.html


\sin: Sine; Example: \sin@@{z}

Will be translated to: Sin[$0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.14#E1

Mathematica: https://reference.wolfram.com/language/ref/Sin.html


E: You use a typical letter for a constant [the mathematical constant e == Napier's constant == 2.71828182845...].

We keep it like it is! But you should know that Mathematica uses E for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \expe


I: You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Mathematica uses I for this constant.

If you want to translate it as a constant, use the corresponding DLMF macro \iunit


e: the mathematical constant e == Napier's constant == 2.71828182845... was translated to: e

i: the imaginary unit == the principal square root of -1 was translated to: i


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