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Power




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.02.19.0036.01









  


  








Input Form





Arg[z^a] == ArcTan[Cos[Im[a] Log[Abs[z]] + ArcTan[Re[z], Im[z]] Re[a]], Sin[Im[a] Log[Abs[z]] + ArcTan[Re[z], Im[z]] Re[a]]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Arg", "[", SuperscriptBox["z", "a"], "]"]], "\[Equal]", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]], "+", RowBox[List[RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ",", RowBox[List["Im", "[", "z", "]"]]]], "]"]], " ", RowBox[List["Re", "[", "a", "]"]]]]]], "]"]], ",", RowBox[List["Sin", "[", RowBox[List[RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]], "+", RowBox[List[RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ",", RowBox[List["Im", "[", "z", "]"]]]], "]"]], " ", RowBox[List["Re", "[", "a", "]"]]]]]], "]"]]]], "]"]]]]]]








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> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <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> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <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> <mo> , </mo> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <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> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <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> <arg /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> </apply> <apply> <arctan /> <apply> <cos /> <apply> <plus /> <apply> <times /> <apply> <imaginary /> <ci> a </ci> </apply> <apply> <ln /> <apply> <abs /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <arctan /> <apply> <real /> <ci> z </ci> </apply> <apply> <imaginary /> <ci> z </ci> </apply> </apply> <apply> <real /> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <sin /> <apply> <plus /> <apply> <times /> <apply> <imaginary /> <ci> a </ci> </apply> <apply> <ln /> <apply> <abs /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <arctan /> <apply> <real /> <ci> z </ci> </apply> <apply> <imaginary /> <ci> z </ci> </apply> </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["Arg", "[", SuperscriptBox["z_", "a_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["Cos", "[", RowBox[List[RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]], "+", RowBox[List[RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ",", RowBox[List["Im", "[", "z", "]"]]]], "]"]], " ", RowBox[List["Re", "[", "a", "]"]]]]]], "]"]], ",", RowBox[List["Sin", "[", RowBox[List[RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]], "+", RowBox[List[RowBox[List["ArcTan", "[", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ",", RowBox[List["Im", "[", "z", "]"]]]], "]"]], " ", RowBox[List["Re", "[", "a", "]"]]]]]], "]"]]]], "]"]]]]]]


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





2001-10-29