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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Transformations > Argument involving complex components





http://functions.wolfram.com/01.06.16.0081.01









  


  








Input Form





Sin[Arg[z]] + I Cos[Arg[z]] == (I Conjugate[z])/Abs[z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Sin", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cos", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]]]]]], "\[Equal]", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Conjugate", "[", "z", "]"]]]], 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> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mover> <mi> z </mi> <mo> _ </mo> </mover> </mrow> <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> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <sin /> <apply> <arg /> <ci> z </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <cos /> <apply> <arg /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <ci> OverBar </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <abs /> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Sin", "[", RowBox[List["Arg", "[", "z_", "]"]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cos", "[", RowBox[List["Arg", "[", "z_", "]"]], "]"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["Conjugate", "[", "z", "]"]]]], RowBox[List["Abs", "[", "z", "]"]]]]]]]


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





2001-10-29