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 Power

 http://functions.wolfram.com/01.02.19.0050.01

 Input Form

 Conjugate[z]^a == z^a E^(2 I a (-Arg[z] + Pi Floor[(Pi + Arg[z])/(2 Pi)]))

 Standard Form

 Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["Conjugate", "[", "z", "]"]], "a"], "\[Equal]", RowBox[List[SuperscriptBox["z", "a"], SuperscriptBox["\[ExponentialE]", RowBox[List["2", "\[ImaginaryI]", " ", "a", " ", RowBox[List["(", 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 _ a z a 2 a ( π arg ( z ) + π 2 π - arg ( z ) ) OverBar z a z a 2 a z 2 -1 -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["Conjugate", "[", "z_", "]"]], "a_"], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", "a"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", RowBox[List["(", 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