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 Power

 http://functions.wolfram.com/01.02.16.0070.01

 Input Form

 z^(I a) == (z^a)^I Exp[2 Pi Floor[(Pi - Im[a Log[z]])/(2 Pi)]]

 Standard Form

 Cell[BoxData[RowBox[List[SuperscriptBox["z", RowBox[List["\[ImaginaryI]", " ", "a"]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "a"], ")"]], "\[ImaginaryI]"], RowBox[List["Exp", "[", RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]], "]"]], " "]]]]]]

 MathML Form

 z a ( z a ) 2 π π - Im ( a log ( z ) ) 2 π z a z a 2 -1 a z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["z_", RowBox[List["\[ImaginaryI]", " ", "a_"]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "a"], ")"]], "\[ImaginaryI]"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]]

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

 2007-05-02