Complex conjugate: Representations through equivalent functions (formula 12.05.27.0004)

Conjugate

$Mathematica Notation$

Complex Components

Conjugate[z]

Representations through equivalent functions

With related functions

With Im

http://functions.wolfram.com/12.05.27.0004.01

Input Form

Conjugate[z] == z - 2 I Im[z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Conjugate", "[", "z", "]"]], "\[Equal]", RowBox[List["z", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", 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> <mover> <mi> z </mi> <mo> _ </mo> </mover> <mo> ⩵ </mo> <mrow> <mi> z </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> OverBar </ci> <ci> z </ci> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <imaginary /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Conjugate", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["z", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["Im", "[", "z", "]"]]]]]]]]]]

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

2007-05-02