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Display information for equation id:math.219374.15 on revision:219374

* Page found: Euler's formula (eq math.219374.15)

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Occurrences on the following pages:

Hash: 8079647a0a73fad84ad9246b7b9b9278

TeX (original user input):

\ln z= \ln |z| + i \phi \ .

TeX (checked):

\ln z=\ln |z|+i\phi \ .

LaTeXML (experimental; uses MathML) rendering

MathML (3.198 KB / 684 B) :

ln z = ln | z | + i ϕ . 𝑧 𝑧 𝑖 italic-ϕ {\displaystyle\ln z=\ln|z|+i\phi\ .}
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SVG (6.253 KB / 2.376 KB) :

ln z equals ln StartAbsoluteValue z EndAbsoluteValue plus i times phi period

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

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :


PNG (0 B / 8 B) :


Translations to Computer Algebra Systems

Translation to Maple

In Maple: ln(z)= 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.


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


Translation to Mathematica

In Mathematica: Log[z]= 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


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.


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


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