(Subscript[z, 1]/Subscript[z, 2])^a == Subscript[z, 1]^a/Subscript[z, 2]^a /; (Arg[Subscript[z, 1]] <= 0 && Arg[Subscript[z, 2]] < Pi + Arg[Subscript[z, 1]]) || (Arg[Subscript[z, 1]] > 0 && Arg[Subscript[z, 2]] >= -Pi + Arg[Subscript[z, 1]])

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> <mo> ) </mo> </mrow> <mi> a </mi> </msup> <mo> &#10869; </mo> <mrow> <msubsup> <mi> z </mi> <mn> 1 </mn> <mi> a </mi> </msubsup> <mo> &#8290; </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> a </mi> </mrow> </msubsup> </mrow> </mrow> <mtext> </mtext> <mo> /; </mo> <mrow> <mrow> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mi> &#960; </mi> </mrow> </mrow> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> <mo> &#8805; </mo> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <ci> a </ci> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <or /> <apply> <and /> <apply> <leq /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <lt /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <pi /> </apply> </apply> </apply> <apply> <and /> <apply> <gt /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <geq /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", FractionBox[SubscriptBox["z_", "1"], SubscriptBox["z_", "2"]], ")"]], "a_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubsuperscriptBox["zz", "1", "a"], " ", SubsuperscriptBox["zz", "2", RowBox[List["-", "a"]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Arg", "[", SubscriptBox["zz", "1"], "]"]], "\[LessEqual]", "0"]], "&&", RowBox[List[RowBox[List["Arg", "[", SubscriptBox["zz", "2"], "]"]], "<", RowBox[List["\[Pi]", "+", RowBox[List["Arg", "[", SubscriptBox["zz", "1"], "]"]]]]]]]], ")"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Arg", "[", SubscriptBox["zz", "1"], "]"]], ">", "0"]], "&&", RowBox[List[RowBox[List["Arg", "[", SubscriptBox["zz", "2"], "]"]], "\[GreaterEqual]", RowBox[List[RowBox[List["-", "\[Pi]"]], "+", RowBox[List["Arg", "[", SubscriptBox["zz", "1"], "]"]]]]]]]], ")"]]]]]]]]]]

2007-05-02