Real part: Representations through equivalent functions (formula 12.03.27.0004)

$Mathematica Notation$

Complex Components

Re[z]

Representations through equivalent functions

With related functions

With Conjugate

http://functions.wolfram.com/12.03.27.0004.01

Input Form

Re[z] == (z + Conjugate[z])/2

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[Equal]", FractionBox[RowBox[List["z", "+", RowBox[List["Conjugate", "[", "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> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mi> z </mi> <mo> + </mo> <mover> <mi> z </mi> <mo> _ </mo> </mover> </mrow> <mn> 2 </mn> </mfrac> <mtext> </mtext> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <real /> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <ci> z </ci> <apply> <ci> OverBar </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Re", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["z", "+", RowBox[List["Conjugate", "[", "z", "]"]]]], ")"]]]]]]]]

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

2001-10-29