Complex conjugate: Representations through equivalent functions (formula 12.05.27.0005)

Conjugate

$Mathematica Notation$

Complex Components

Conjugate[z]

Representations through equivalent functions

With related functions

With Abs

http://functions.wolfram.com/12.05.27.0005.01

Input Form

Conjugate[z] == Abs[z]^2/z

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Conjugate", "[", "z", "]"]], "\[Equal]", FractionBox[SuperscriptBox[RowBox[List["Abs", "[", "z", "]"]], "2"], "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> <mi> z </mi> <mo> _ </mo> </mover> <mo> ⩵ </mo> <mfrac> <msup> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mn> 2 </mn> </msup> <mi> z </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> OverBar </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <apply> <abs /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

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

2007-05-02