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Display information for equation id:math.219374.45 on revision:219374

* Page found: Euler's formula (eq math.219374.45)

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Occurrences on the following pages:

Hash: b656a8820b1dd231ab2b7578f0e9998d

TeX (original user input):

r (\cos(\theta) + i \sin(\theta))

TeX (checked):

r(\cos(\theta )+i\sin(\theta ))

LaTeXML (experimental; uses MathML) rendering

MathML (3.412 KB / 689 B) :

r ( cos ( θ ) + i sin ( θ ) ) 𝑟 𝜃 𝑖 𝜃 {\displaystyle r(\cos(\theta)+i\sin(\theta))}
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SVG (7.714 KB / 2.857 KB) :

r times left-parenthesis cosine left-parenthesis theta right-parenthesis plus i times sine left-parenthesis theta right-parenthesis right-parenthesis

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

MathML (0 B / 8 B) :

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Translations to Computer Algebra Systems

Translation to Maple

In Maple: r*(cos(theta)+ i*sin(theta))

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


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


Translation to Mathematica

In Mathematica: r*(Cos[\[Theta]]+ i*Sin[\[Theta]])

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


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


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


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