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Display information for equation id:math.219374.54 on revision:219374

* Page found: Euler's formula (eq math.219374.54)

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Hash: 62c987e6d2b2dd8e282e298a35724d00

TeX (original user input):

e^{ix} = 1(\cos(x)+i \sin(x))

TeX (checked):

e^{ix}=1(\cos(x)+i\sin(x))

LaTeXML (experimental; uses MathML) rendering

MathML (4.815 KB / 900 B) :

e i x = 1 ( cos ( x ) + i sin ( x ) ) superscript 𝑒 𝑖 𝑥 1 𝑥 𝑖 𝑥 {\displaystyle e^{{ix}}=1(\cos(x)+i\sin(x))}
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SVG (9.244 KB / 3.31 KB) :

e Superscript i times x Baseline equals 1 times left-parenthesis cosine left-parenthesis x right-parenthesis plus i times sine left-parenthesis x right-parenthesis right-parenthesis

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

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: (e)^(i*x)= 1*(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)= 1*(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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