z^Conjugate[a] == z^(a Exp[-2 I Arg[a]])

Cell[BoxData[RowBox[List[SuperscriptBox["z", RowBox[List["Conjugate", "[", "a", "]"]]], "\[Equal]", SuperscriptBox["z", RowBox[List["a", " ", RowBox[List["Exp", "[", RowBox[List[RowBox[List["-", "2"]], " ", "I", " ", RowBox[List["Arg", "[", "a", "]"]]]], "]"]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mi> z </mi> <mover> <mi> a </mi> <mo> _ </mo> </mover> </msup> <mo> &#10869; </mo> <msup> <mi> z </mi> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> </msup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <ci> z </ci> <apply> <ci> OverBar </ci> <ci> a </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> <apply> <arg /> <ci> a </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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

2007-05-02