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Display information for equation id:math.219374.14 on revision:219374

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TeX (original user input):

 z = |z| e^{i \phi} = e^{\ln |z|} e^{i \phi} = e^{\ln |z| + i \phi} \

TeX (checked):

z=|z|e^{i\phi }=e^{\ln |z|}e^{i\phi }=e^{\ln |z|+i\phi }\

LaTeXML (experimental; uses MathML) rendering

MathML (8.606 KB / 1.285 KB) :

z = | z | e i ϕ = e ln | z | e i ϕ = e ln | z | + i ϕ 𝑧 𝑧 superscript 𝑒 𝑖 italic-ϕ superscript 𝑒 𝑧 superscript 𝑒 𝑖 italic-ϕ superscript 𝑒 𝑧 𝑖 italic-ϕ {\displaystyle z=|z|e^{{i\phi}}=e^{{\ln|z|}}e^{{i\phi}}=e^{{\ln|z|+i\phi}}\ }
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SVG (9.745 KB / 2.848 KB) :

z equals StartAbsoluteValue z EndAbsoluteValue times e Superscript i times phi Baseline equals e Superscript ln StartAbsoluteValue z EndAbsoluteValue Baseline times e Superscript i times phi Baseline equals e Superscript ln StartAbsoluteValue z EndAbsoluteValue plus i times phi

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: z =abs(z)* (e)^(i*phi)= (e)^(ln(abs(z)))* (e)^(i*phi)= (e)^(ln(abs(z))+ i*phi)

Information about the conversion process:

\ln: Natural logarithm; Example: \ln@@{z}

Will be translated to: ln($0)

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

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


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


\phi: Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.

But this system don't know how to translate it as a constant. It was translated as a general letter.


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: z =Abs[z]* (e)^(i*\[Phi])= (e)^(Log[Abs[z]])* (e)^(i*\[Phi])= (e)^(Log[Abs[z]]+ i*\[Phi])

Information about the conversion process:

\ln: Natural logarithm; Example: \ln@@{z}

Will be translated to: Log[$0]

Constraints: z != 0

Branch Cuts: (-\infty, 0]

Relevant links to definitions:

DLMF: http://dlmf.nist.gov/4.2#E2

Mathematica: https://reference.wolfram.com/language/ref/Log.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


\phi: Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.

But this system don't know how to translate it as a constant. It was translated as a general letter.


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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