Imaginary part: Complex characteristics (formula 12.04.19.0009)

$Mathematica Notation$

Complex Components

Im[z]

Complex characteristics

Absolute value

http://functions.wolfram.com/12.04.19.0009.01

Input Form

Abs[Im[z]] == Sqrt[Im[z]^2]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "\[Equal]", SqrtBox[SuperscriptBox[RowBox[List["Im", "[", "z", "]"]], "2"]]]]]]

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> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ⩵ </mo> <msqrt> <msup> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <apply> <imaginary /> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", RowBox[List["Im", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", SqrtBox[SuperscriptBox[RowBox[List["Im", "[", "z", "]"]], "2"]]]]]]

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

2007-05-02