Degree: Representations through equivalent functions (formula 02.04.27.0007)

Degree

$Mathematica Notation$

Constants

Degree

Representations through equivalent functions

With related functions

http://functions.wolfram.com/02.04.27.0007.01

Input Form

E^(90 Degree I k) == I^k /; Element[k, Integers]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["90", " ", "Degree", " ", "\[ImaginaryI]", " ", "k"]]], "\[Equal]", SuperscriptBox["\[ImaginaryI]", "k"]]], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mn> 90 </mn> <mo> ⁢ </mo> <mo> ° </mo> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> k </mi> </mrow> </msup> <mo> ⩵ </mo> <msup> <mi> ⅈ </mi> <mi> k </mi> </msup> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> ∈ </mo> <semantics> <mi> ℤ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 90 </cn> <ci> Degree </ci> <imaginaryi /> <ci> k </ci> </apply> </apply> <apply> <power /> <imaginaryi /> <ci> k </ci> </apply> </apply> <apply> <in /> <ci> k </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox["\[ExponentialE]", RowBox[List["90", " ", "\[Degree]", " ", "\[ImaginaryI]", " ", "k_"]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["\[ImaginaryI]", "k"], "/;", RowBox[List["k", "\[Element]", "Integers"]]]]]]]]

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

2007-05-02