Sign[Sqrt[3] + I] == (Sqrt[3] + I)/2

Cell[BoxData[RowBox[List[RowBox[List["Sign", "[", RowBox[List[SqrtBox["3"], "+", "\[ImaginaryI]"]], "]"]], "\[Equal]", FractionBox[RowBox[List[SqrtBox["3"], "+", "\[ImaginaryI]"]], "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> <msqrt> <mn> 3 </mn> </msqrt> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <msqrt> <mn> 3 </mn> </msqrt> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Sign </ci> <apply> <plus /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sign", "[", RowBox[List[SqrtBox["3"], "+", "\[ImaginaryI]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[SqrtBox["3"], "+", "\[ImaginaryI]"]], ")"]]]]]]]]

2007-05-02