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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Complex characteristics > Argument





http://functions.wolfram.com/01.02.19.0031.01









  


  








Input Form





Arg[z^a] == Im[a Log[z]] /; Inequality[-(Pi/Log[z]), Less, Im[a], LessEqual, Pi/Log[z]] && z > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Arg", "[", SuperscriptBox["z", "a"], "]"]], "\[Equal]", RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", RowBox[List["Log", "[", "z", "]"]]]]], "<", RowBox[List["Im", "[", "a", "]"]], "\[LessEqual]", FractionBox["\[Pi]", RowBox[List["Log", "[", "z", "]"]]]]], "\[And]", RowBox[List["z", ">", "0"]]]]]]]]








MathML Form







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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Arg", "[", SuperscriptBox["z_", "a_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Im", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", RowBox[List["Log", "[", "z", "]"]]]]], "<", RowBox[List["Im", "[", "a", "]"]], "\[LessEqual]", FractionBox["\[Pi]", RowBox[List["Log", "[", "z", "]"]]]]], "&&", RowBox[List["z", ">", "0"]]]]]]]]]]


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





2001-10-29