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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Complex characteristics > Argument





http://functions.wolfram.com/01.03.19.0015.01









  


  








Input Form





Abs[E^z] == ArcTan[Cos[Im[z]], Sin[Im[z]]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", SuperscriptBox["\[ExponentialE]", "z"], "]"]], "\[Equal]", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["Cos", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], ",", RowBox[List["Sin", "[", RowBox[List["Im", "[", "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> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msup> <mi> &#8519; </mi> <mi> z </mi> </msup> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <arctan /> <apply> <cos /> <apply> <imaginary /> <ci> z </ci> </apply> </apply> <apply> <sin /> <apply> <imaginary /> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["Cos", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], ",", RowBox[List["Sin", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]], "]"]]]]]]


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





2007-05-02