Coth[(Pi I)/30] == (-I) Sqrt[23 + 10 Sqrt[5] + 2 Sqrt[255 + 114 Sqrt[5]]]

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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> <mrow> <mi> coth </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 30 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 23 </mn> <mo> + </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 255 </mn> <mo> + </mo> <mrow> <mn> 114 </mn> <mo> &#8290; </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> </mrow> </msqrt> </mrow> </mrow> </msqrt> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <coth /> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 30 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 23 </cn> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 255 </cn> <apply> <times /> <cn type='integer'> 114 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Coth", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "30"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SqrtBox[RowBox[List["23", "+", RowBox[List["10", " ", SqrtBox["5"]]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["255", "+", RowBox[List["114", " ", SqrtBox["5"]]]]]]]]]]]]]]]]]

2001-10-29