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 Log

 http://functions.wolfram.com/01.04.16.0047.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Log", "[", RowBox[List["Conjugate", "[", "z", "]"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", 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"]]], "]"]]]]]], ")"]]]]]]]]]]

 MathML Form

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

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["Conjugate", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Log", "[", "z", "]"]], "-", 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