(z^n)^(1/n) == z /; Inequality[-(Pi/n), Less, Arg[z], LessEqual, Pi/n] && Element[n, Integers] && n > 0

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", "n"], ")"]], RowBox[List["1", "/", "n"]]], "\[Equal]", "z"]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "n"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "n"]]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "0"]]]]]]]]

<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> <msup> <mi> z </mi> <mi> n </mi> </msup> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> / </mo> <mi> n </mi> </mrow> </msup> <mo> &#10869; </mo> <mi> z </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#960; </mi> <mi> n </mi> </mfrac> </mrow> <mo> &lt; </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mfrac> <mi> &#960; </mi> <mi> n </mi> </mfrac> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox[&quot;\[DoubleStruckCapitalN]&quot;, &quot;+&quot;], Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <and /> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <lt /> <apply> <arg /> <ci> z </ci> </apply> <leq /> <apply> <times /> <pi /> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", SuperscriptBox["z_", "n_"], ")"]], FractionBox["1", "n_"]], "]"]], "\[RuleDelayed]", RowBox[List["z", "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "n"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "n"]]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]]

2001-10-29