Sign[Im[z]] == Im[z]/Sqrt[Im[z]^2]

Cell[BoxData[RowBox[List[RowBox[List["Sign", "[", RowBox[List["Im", "[", "z", "]"]], "]"]], "\[Equal]", FractionBox[RowBox[List["Im", "[", "z", "]"]], SqrtBox[SuperscriptBox[RowBox[List["Im", "[", "z", "]"]], "2"]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <msqrt> <msup> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </msqrt> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Sign </ci> <apply> <imaginary /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <imaginary /> <ci> z </ci> </apply> <apply> <power /> <apply> <power /> <apply> <power /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sign", "[", RowBox[List["Im", "[", "z_", "]"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Im", "[", "z", "]"]], SqrtBox[SuperscriptBox[RowBox[List["Im", "[", "z", "]"]], "2"]]]]]]]

2007-05-02