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Conjugate




Mathematica Notation

Traditional Notation









Complex Components > Conjugate[z] > Specific values > Specialized values





http://functions.wolfram.com/12.05.03.0003.01









  


  








Input Form





Conjugate[x + I y] == x - I y /; Element[x, Reals] && Element[y, Reals]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "\[Equal]", RowBox[List["x", "-", RowBox[List["\[ImaginaryI]", " ", "y"]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mover> <mrow> <mi> x </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> <mo> _ </mo> </mover> <mo> &#10869; </mo> <mrow> <mi> x </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> y </mi> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> x </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> y </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> OverBar </ci> <apply> <plus /> <ci> x </ci> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> <apply> <plus /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> x </ci> <reals /> </apply> <apply> <in /> <ci> y </ci> <reals /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Conjugate", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["x", "-", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]]]


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





2001-10-29