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Arg




Mathematica Notation

Traditional Notation









Complex Components > Arg[z] > Transformations > Power of arguments





http://functions.wolfram.com/12.02.16.0026.01









  


  








Input Form





Arg[z^a] == Re[a] Arg[z] + Im[a] Log[Abs[z]] + 2 Pi Floor[(Pi - Im[a] Log[Abs[z]] - Arg[z] Re[a])/(2 Pi)]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Arg", "[", SuperscriptBox["z", "a"], "]"]], "\[Equal]", " ", 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", "]"]], "]"]]]], "+", RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]], "-", RowBox[List[RowBox[List["Arg", "[", "z", "]"]], " ", RowBox[List["Re", "[", "a", "]"]]]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]








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> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mi> Im </mi> <mo> &#8290; </mo> <mrow> <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> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> - </mo> <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> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arg /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <real /> <ci> a </ci> </apply> <apply> <arg /> <ci> z </ci> </apply> </apply> <apply> <times /> <imaginary /> <ci> a </ci> <apply> <ln /> <apply> <abs /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <imaginary /> <ci> a </ci> </apply> <apply> <ln /> <apply> <abs /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <arg /> <ci> z </ci> </apply> <apply> <real /> <ci> a </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </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[RowBox[List[RowBox[List["Re", "[", "a", "]"]], " ", RowBox[List["Arg", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]], "+", RowBox[List["2", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List[RowBox[List["Im", "[", "a", "]"]], " ", RowBox[List["Log", "[", RowBox[List["Abs", "[", "z", "]"]], "]"]]]], "-", RowBox[List[RowBox[List["Arg", "[", "z", "]"]], " ", RowBox[List["Re", "[", "a", "]"]]]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]


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





2001-10-29