Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Specific values > Values at fixed points





http://functions.wolfram.com/01.03.03.0133.01









  


  








Input Form





E^((9 Pi I)/7) == (-2 2^(1/3) Sqrt[7] (-I + Sqrt[3]) + (1 - I Sqrt[3]) (28 - 2 I Sqrt[7] - 6 Sqrt[21])^(2/3) + (2 - 2 I Sqrt[7]) (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3))/ (12 (14 - I Sqrt[7] - 3 Sqrt[21])^(1/3))








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["9", "\[Pi]", " ", "\[ImaginaryI]"]], "7"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SqrtBox["7"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], ")"]], "/", RowBox[List["(", RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mi> &#8519; </mi> <mfrac> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> <mn> 7 </mn> </mfrac> </msup> <mo> &#10869; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mn> 7 </mn> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mroot> <mrow> <mn> 14 </mn> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mn> 7 </mn> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msqrt> <mn> 21 </mn> </msqrt> </mrow> </mrow> <mn> 3 </mn> </mroot> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 28 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mn> 7 </mn> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msqrt> <mn> 21 </mn> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mroot> <mn> 2 </mn> <mn> 3 </mn> </mroot> <mo> &#8290; </mo> <msqrt> <mn> 7 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> + </mo> <msqrt> <mn> 3 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mroot> <mrow> <mn> 14 </mn> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <msqrt> <mn> 7 </mn> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <msqrt> <mn> 21 </mn> </msqrt> </mrow> </mrow> <mn> 3 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 9 </cn> <pi /> <imaginaryi /> <apply> <power /> <cn type='integer'> 7 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> 7 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 14 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 7 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> 21 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 28 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <power /> <cn type='integer'> 7 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <power /> <cn type='integer'> 21 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 7 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 14 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 7 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <cn type='integer'> 21 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["9", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "7"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", SqrtBox["7"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", SqrtBox["3"]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["3"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["28", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["6", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["2", "/", "3"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox["7"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]]]], RowBox[List["12", " ", SuperscriptBox[RowBox[List["(", RowBox[List["14", "-", RowBox[List["\[ImaginaryI]", " ", SqrtBox["7"]]], "-", RowBox[List["3", " ", SqrtBox["21"]]]]], ")"]], RowBox[List["1", "/", "3"]]]]]]]]]]


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





2001-10-29