z^a == z^(a + (2 I Pi)/Log[z])

Cell[BoxData[RowBox[List[SuperscriptBox["z", "a"], "\[Equal]", SuperscriptBox["z", RowBox[List["a", "+", FractionBox[RowBox[List["2", " ", "I", " ", "\[Pi]"]], RowBox[List["Log", "[", "z", "]"]]]]]]]]]]

<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> <mi> a </mi> </msup> <mo> &#10869; </mo> <msup> <mi> z </mi> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> </msup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <pi /> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["z_", "a_"], "]"]], "\[RuleDelayed]", SuperscriptBox["z", RowBox[List["a", "+", FractionBox[RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]"]], RowBox[List["Log", "[", "z", "]"]]]]]]]]]]

2001-10-29