Absolute value function: Complex characteristics (formula 12.01.19.0010)

Abs

$Mathematica Notation$

Complex Components

Abs[z]

Complex characteristics

Conjugate value

http://functions.wolfram.com/12.01.19.0010.01

Input Form

Conjugate[Abs[z]] == Abs[z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]], "\[Equal]", 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> <mover> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> _ </mo> </mover> <mo> ⩵ </mo> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> OverBar </ci> <apply> <abs /> <ci> z </ci> </apply> </apply> <apply> <abs /> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Conjugate", "[", RowBox[List["Abs", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Abs", "[", "z", "]"]]]]]]

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

2001-10-29