Argument: Representations through equivalent functions (formula 12.02.27.0002)

Arg

$Mathematica Notation$

Complex Components

Arg[z]

Representations through equivalent functions

With related functions

With Abs

http://functions.wolfram.com/12.02.27.0002.01

Input Form

Cos[Arg[z]] == Re[z]/Abs[z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Cos", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "\[Equal]", FractionBox[RowBox[List["Re", "[", "z", "]"]], RowBox[List["Abs", "[", "z", "]"]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <cos /> <apply> <arg /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <real /> <ci> z </ci> </apply> <apply> <power /> <apply> <abs /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cos", "[", RowBox[List["Arg", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Re", "[", "z", "]"]], RowBox[List["Abs", "[", "z", "]"]]]]]]]

Date Added to functions.wolfram.com (modification date)

2001-10-29