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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Complex characteristics > Signum value





http://functions.wolfram.com/01.02.19.0048.01









  


  








Input Form





Sign[z^a] == E^(I (Re[a] Arg[z] + Im[a] Log[Abs[z]]))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Sign", "[", SuperscriptBox["z", "a"], "]"]], "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Re", "[", "a", "]"]], " ", RowBox[List["Arg", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]]]], ")"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> exp </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> z </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Sign </ci> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> </apply> <apply> <exp /> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <apply> <imaginary /> <ci> a </ci> </apply> <apply> <ln /> <apply> <abs /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <arg /> <ci> z </ci> </apply> <apply> <real /> <ci> a </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sign", "[", SuperscriptBox["z_", "a_"], "]"]], "]"]], "\[RuleDelayed]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Re", "[", "a", "]"]], " ", RowBox[List["Arg", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]]]], ")"]]]]]]]]]


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





2001-10-29