Im[Log[z]] == Arg[z]

Cell[BoxData[RowBox[List[RowBox[List["Im", "[", RowBox[List["Log", "[", "z", "]"]], "]"]], "\[Equal]", RowBox[List["Arg", "[", "z", "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <imaginary /> <apply> <ln /> <ci> z </ci> </apply> </apply> <apply> <arg /> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Im", "[", RowBox[List["Log", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Arg", "[", "z", "]"]]]]]]

2007-05-02