Sqrt[Subscript[z, 1]/Subscript[z, 2]] == Sqrt[-Subscript[z, 1]] Sqrt[-(1/Subscript[z, 2])] /; Subscript[z, 1] + Subscript[z, 2] < 0

Cell[BoxData[RowBox[List[RowBox[List[SqrtBox[FractionBox[SubscriptBox["z", "1"], SubscriptBox["z", "2"]]], "\[Equal]", RowBox[List[SqrtBox[RowBox[List["-", SubscriptBox["z", "1"]]]], SqrtBox[RowBox[List["-", FractionBox["1", SubscriptBox["z", "2"]]]]]]]]], "/;", " ", RowBox[List[RowBox[List[SubscriptBox["z", "1"], "+", " ", SubscriptBox["z", "2"]]], "<", "0"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msqrt> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> </msqrt> <mo> &#10869; </mo> <mrow> <msqrt> <mrow> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> </mrow> </msqrt> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <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> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <lt /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SqrtBox[FractionBox[SubscriptBox["z_", "1"], SubscriptBox["z_", "2"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox[RowBox[List["-", SubscriptBox["zz", "1"]]]], " ", SqrtBox[RowBox[List["-", FractionBox["1", SubscriptBox["zz", "2"]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["zz", "1"], "+", SubscriptBox["zz", "2"]]], "<", "0"]]]]]]]]

2001-10-29