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 Arg

 http://functions.wolfram.com/12.02.16.0005.01

 Input Form

 Arg[(-I) z] == Arg[z] + Pi/2 - ((-1)^(1/4) Pi Sqrt[(-I) z])/Sqrt[z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Arg", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "+", FractionBox["\[Pi]", "2"], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "\[Pi]", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]]]], SqrtBox["z"]]]]]]]]

 MathML Form

 arg ( - z ) arg ( z ) + π 2 - - 1 4 π - z z -1 z z 2 -1 -1 -1 1 4 -1 z 1 2 z 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Arg", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Arg", "[", "z", "]"]], "+", FractionBox["\[Pi]", "2"], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "\[Pi]", " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]]]], SqrtBox["z"]]]]]]]]

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

 2001-10-29