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http://functions.wolfram.com/01.03.03.0208.01
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E^((Pi I)/30) == (1/8) (Sqrt[3] + Sqrt[15] + Sqrt[10 - 2 Sqrt[5]]) +
I (1/8) (Sqrt[30 - 6 Sqrt[5]] - Sqrt[5] - 1)
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Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "30"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[SqrtBox["3"], "+", SqrtBox["15"], "+", SqrtBox[RowBox[List["10", "-", RowBox[List["2", " ", SqrtBox["5"]]]]]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["30", "-", RowBox[List["6", " ", SqrtBox["5"]]]]]], "-", SqrtBox["5"], "-", "1"]], ")"]]]]]]]]]]
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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> <msup> <mi> ⅇ </mi> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> <mn> 30 </mn> </mfrac> </msup> <mo> ⩵ </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 10 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> </mrow> </msqrt> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> <mo> + </mo> <msqrt> <mn> 15 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mi> ⅈ </mi> <mn> 8 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 30 </mn> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> ⁢ </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> </mrow> </msqrt> <mo> - </mo> <msqrt> <mn> 5 </mn> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <times /> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 30 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 10 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 15 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 30 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "30"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[SqrtBox["3"], "+", SqrtBox["15"], "+", SqrtBox[RowBox[List["10", "-", RowBox[List["2", " ", SqrtBox["5"]]]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", "8"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["30", "-", RowBox[List["6", " ", SqrtBox["5"]]]]]], "-", SqrtBox["5"], "-", "1"]], ")"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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