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Display information for equation id:math.223294.15 on revision:223294

* Page found: Box–Muller transform (eq math.223294.15)

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Hash: 266abe80af4999d44cf72ce102be83e1

TeX (original user input):

\mathrm{exp}(iz) = e^{i z} = \cos(z) + i \sin(z), \,

TeX (checked):

\mathrm {exp} (iz)=e^{iz}=\cos(z)+i\sin(z),\,

LaTeXML (experimental; uses MathML) rendering

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exp ( i z ) = e i z = cos ( z ) + i sin ( z ) , exp i z superscript e i z z i z {\displaystyle{\mathrm{exp}}(iz)=e^{{iz}}=\cos(z)+i\sin(z),\,}
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SVG (11.671 KB / 4.16 KB) :

exp times left-parenthesis i times z right-parenthesis equals e Superscript i times z Baseline equals cosine left-parenthesis z right-parenthesis plus i times sine left-parenthesis z right-parenthesis comma

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: exp(i*z)= (e)^(i*z)= cos(z)+ i*sin(z),

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


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 Maple uses exp(1) for this constant.

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


exp: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

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



Translation to Mathematica

In Mathematica: exp(i*z)= (e)^(i*z)= Cos[z]+ i*Sin[z],

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


exp: Function without DLMF-Definition. We cannot translate it and keep it like it is (but delete prefix \ if necessary).

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



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