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 Conjugate

 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

 z _ z - 2 ( arg ( z ) - π arg ( z ) + π 2 π ) OverBar z z -2 z -1 z 2 -1 [/itex]

 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