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Arg




Mathematica Notation

Traditional Notation









Complex Components > Arg[z] > Transformations > Products, sums, and powers of the direct function > Differences of the direct function





http://functions.wolfram.com/12.02.16.0100.01









  


  








Input Form





Arg[Subscript[z, 1]] - Arg[Subscript[z, 2]] == Arg[Subscript[z, 1]/Subscript[z, 2]] /; Inequality[-Pi, Less, Arg[Subscript[z, 1]] - Arg[Subscript[z, 2]], LessEqual, Pi]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["Arg", "[", SubscriptBox["z", "1"], "]"]], "-", RowBox[List["Arg", "[", SubscriptBox["z", "2"], "]"]]]], "\[Equal]", RowBox[List["Arg", "[", FractionBox[SubscriptBox["z", "1"], SubscriptBox["z", "2"]], "]"]]]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List[RowBox[List["Arg", "[", SubscriptBox["z", "1"], "]"]], "-", RowBox[List["Arg", "[", SubscriptBox["z", "2"], "]"]]]], "\[LessEqual]", "\[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> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mo> &lt; </mo> <mrow> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#8804; </mo> <mi> &#960; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <arg /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <lt /> <apply> <plus /> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <leq /> <pi /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Arg", "[", SubscriptBox["z_", "1"], "]"]], "-", RowBox[List["Arg", "[", SubscriptBox["z_", "2"], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Arg", "[", FractionBox[SubscriptBox["zz", "1"], SubscriptBox["zz", "2"]], "]"]], "/;", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List[RowBox[List["Arg", "[", SubscriptBox["zz", "1"], "]"]], "-", RowBox[List["Arg", "[", SubscriptBox["zz", "2"], "]"]]]], "\[LessEqual]", "\[Pi]"]]]]]]]]


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





2007-05-02