Csch[(13 Pi I)/9] == Root[64 + 96 #1^2 + 36 #1^4 + 3 #1^6 & , 4]

Cell[BoxData[RowBox[List[RowBox[List["Csch", "[", FractionBox[RowBox[List["13", "\[Pi]", " ", "\[ImaginaryI]"]], "9"], "]"]], "\[Equal]", RowBox[List["Root", "[", RowBox[List[RowBox[List[RowBox[List["64", "+", RowBox[List["96", " ", SuperscriptBox["#1", "2"]]], "+", RowBox[List["36", " ", SuperscriptBox["#1", "4"]]], "+", RowBox[List["3", " ", SuperscriptBox["#1", "6"]]]]], "&"]], ",", "4"]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> csch </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mn> 13 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 9 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 36 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 96 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mn> 64 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <csch /> <apply> <times /> <cn type='integer'> 13 </cn> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 9 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 96 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 64 </cn> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Csch", "[", FractionBox[RowBox[List["13", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "9"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Root", "[", RowBox[List[RowBox[List[RowBox[List["64", "+", RowBox[List["96", " ", SuperscriptBox["#1", "2"]]], "+", RowBox[List["36", " ", SuperscriptBox["#1", "4"]]], "+", RowBox[List["3", " ", SuperscriptBox["#1", "6"]]]]], "&"]], ",", "4"]], "]"]]]]]]

2001-10-29