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http://functions.wolfram.com/01.01.16.0069.01
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Sqrt[Subscript[z, 1]/Subscript[z, 2]] ==
(Sqrt[Subscript[z, 1]]/Sqrt[Subscript[z, 2]])
E^(I Pi Floor[(Pi - Arg[Subscript[z, 1]] + Arg[Subscript[z, 2]])/(2 Pi)])
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Cell[BoxData[RowBox[List[SqrtBox[FractionBox[SubscriptBox["z", "1"], RowBox[List[" ", SubscriptBox["z", "2"]]]]], "\[Equal]", " ", RowBox[List[FractionBox[SqrtBox[SubscriptBox["z", "1"]], SqrtBox[SubscriptBox["z", "2"]]], SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Arg", "[", SubscriptBox["z", "1"], "]"]], "+", RowBox[List["Arg", "[", SubscriptBox["z", "2"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]]]]]]
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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> <msqrt> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> </msqrt> <mo> ⩵ </mo> <mrow> <mfrac> <msqrt> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </msqrt> <msqrt> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </msqrt> </mfrac> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mrow> <mi> π </mi> <mo> - </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> arg </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mfrac> <mo> ⌋ </mo> </mrow> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <arg /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SqrtBox[FractionBox[SubscriptBox["z_", "1"], SubscriptBox["z_", "2"]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[SubscriptBox["zz", "1"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["\[Pi]", "-", RowBox[List["Arg", "[", SubscriptBox["zz", "1"], "]"]], "+", RowBox[List["Arg", "[", SubscriptBox["zz", "2"], "]"]]]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]]]], SqrtBox[SubscriptBox["zz", "2"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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