Argument: Transformations (formula 12.02.16.0082)

Arg

$Mathematica Notation$

Complex Components

Arg[z]

Transformations

Exponent of arguments

http://functions.wolfram.com/12.02.16.0082.01

Input Form

Arg[E^z] == Im[z] /; Inequality[-Pi, Less, Im[z], LessEqual, Pi]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Arg", "[", SuperscriptBox["\[ExponentialE]", "z"], "]"]], "\[Equal]", RowBox[List["Im", "[", "z", "]"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mi> π </mi> </mrow> <mo> < </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ≤ </mo> <mi> π </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <arg /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <imaginary /> <ci> z </ci> </apply> </apply> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <lt /> <apply> <imaginary /> <ci> z </ci> </apply> <leq /> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Arg", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Im", "[", "z", "]"]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Im", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]

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

2007-05-02