Sqrt[-z^2] == Sqrt[z] Sqrt[-z]

Cell[BoxData[RowBox[List[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], "\[Equal]", RowBox[List[SqrtBox["z"], " ", SqrtBox[RowBox[List["-", "z"]]]]]]]]]

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

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SqrtBox[RowBox[List["-", SuperscriptBox["z_", "2"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox["z"], " ", SqrtBox[RowBox[List["-", "z"]]]]]]]]]

2001-10-29