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Sqrt




Mathematica Notation

Traditional Notation









Elementary Functions > Sqrt[z] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/01.01.16.0001.01









  


  








Input Form





Sqrt[-z] == (-I) Sqrt[z] /; Im[z] > 0 || (Im[z] == 0 && Re[z] < 0)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SqrtBox[RowBox[List["-", "z"]]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SqrtBox["z"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <or /> <apply> <gt /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <eq /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <lt /> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SqrtBox[RowBox[List["-", "z_"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SqrtBox["z"]]], "/;", RowBox[List[RowBox[List[RowBox[List["Im", "[", "z", "]"]], ">", "0"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Im", "[", "z", "]"]], "\[Equal]", "0"]], "&&", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]], ")"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29