DirectedInfinity[1 + I] == DirectedInfinity[(1 + I)/Sqrt[2]]

Cell[BoxData[RowBox[List[RowBox[List["DirectedInfinity", "[", RowBox[List["1", "+", "\[ImaginaryI]"]], "]"]], "\[Equal]", RowBox[List["DirectedInfinity", "[", FractionBox[RowBox[List["1", "+", "\[ImaginaryI]"]], SqrtBox["2"]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#8734; </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> DirectedInfinity </ci> <cn type='complex-cartesian'> 1 <sep /> 1 </cn> </apply> </annotation-xml> </semantics> <mo> &#10869; </mo> <semantics> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <msqrt> <mn> 2 </mn> </msqrt> </mfrac> <mo> &#8290; </mo> <mi> &#8734; </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> DirectedInfinity </ci> <cn type='complex-cartesian'> 1 <sep /> 1 </cn> </apply> </annotation-xml> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> DirectedInfinity </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> <apply> <ci> DirectedInfinity </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", TagBox[RowBox[List[TagBox[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], "DirectedInfinityCoefficient", Rule[Editable, True]], " ", "\[Infinity]"]], DirectedInfinity, Rule[Editable, False]], "]"]], "\[RuleDelayed]", RowBox[List["DirectedInfinity", "[", FractionBox[RowBox[List["1", "+", "\[ImaginaryI]"]], SqrtBox["2"]], "]"]]]]]]

2001-10-29