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http://functions.wolfram.com/12.06.16.0026.01
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Sign[E^(x + I y)] == E^(I y)
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Cell[BoxData[RowBox[List[RowBox[List["Sign", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]]], "]"]], "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "y"]]]]]]]
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<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> ⁡ </mo> <mo> ( </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> y </mi> </mrow> </mrow> </msup> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> y </mi> </mrow> </msup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Sign </ci> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> x </ci> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sign", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]]], "]"]], "]"]], "\[RuleDelayed]", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "y"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
