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Conjugate




Mathematica Notation

Traditional Notation









Complex Components > Conjugate[z] > Representations through equivalent functions > With related functions > With Arg





http://functions.wolfram.com/12.05.27.0007.01









  


  








Input Form





Conjugate[z] == z Exp[-2 I (Arg[z] - Pi Floor[(Pi + Arg[z])/(2 Pi)])]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Conjugate", "[", "z", "]"]], "\[Equal]", RowBox[List["z", " ", RowBox[List["Exp", "[", RowBox[List[RowBox[List["-", "2"]], " ", "I", " ", RowBox[List["(", RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "-", RowBox[List["Pi", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Pi", "+", RowBox[List["Arg", "[", "z", "]"]]]], RowBox[List["2", "Pi"]]], "]"]]]]]], ")"]]]], "]"]]]]]]]]








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> &#10869; </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> + </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> OverBar </ci> <ci> z </ci> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> <apply> <plus /> <apply> <arg /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <arg /> <ci> z </ci> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </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", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "-", RowBox[List["\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", "z", "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]], ")"]]]]]]]]]]]


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





2007-05-02