Exponential function: Complex characteristics (formula 01.03.19.0011)

Exp

$Mathematica Notation$

Elementary Functions

Exp[z]

Complex characteristics

Absolute value

http://functions.wolfram.com/01.03.19.0011.01

Input Form

Abs[E^z] == E^Re[z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", SuperscriptBox["\[ExponentialE]", "z"], "]"]], "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["Re", "[", "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> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ⩵ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </msup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <real /> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", SuperscriptBox["\[ExponentialE]", "z_"], "]"]], "]"]], "\[RuleDelayed]", SuperscriptBox["\[ExponentialE]", RowBox[List["Re", "[", "z", "]"]]]]]]]

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

2007-05-02