Real part: Transformations (formula 12.03.16.0024)

$Mathematica Notation$

Complex Components

Re[z]

Transformations

Ratio of arguments

http://functions.wolfram.com/12.03.16.0024.01

Input Form

Re[Subscript[z, 1]/Subscript[z, 2]] == (Re[Subscript[z, 1]] Re[Subscript[z, 2]] + Im[Subscript[z, 1]] Im[Subscript[z, 2]])/Abs[Subscript[z, 2]]^2

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Re", "[", FractionBox[SubscriptBox["z", "1"], SubscriptBox["z", "2"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List[RowBox[List["Re", "[", SubscriptBox["z", "1"], "]"]], " ", RowBox[List["Re", "[", SubscriptBox["z", "2"], "]"]]]], "+", RowBox[List[RowBox[List["Im", "[", SubscriptBox["z", "1"], "]"]], " ", RowBox[List["Im", "[", SubscriptBox["z", "2"], "]"]]]]]], SuperscriptBox[RowBox[List["Abs", "[", SubscriptBox["z", "2"], "]"]], "2"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mtext> </mtext> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ) </mo> </mrow> </mrow> </mrow> <msup> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <real /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <real /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <real /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <imaginary /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <imaginary /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <abs /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Re", "[", FractionBox[SubscriptBox["z_", "1"], SubscriptBox["z_", "2"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["Re", "[", SubscriptBox["zz", "1"], "]"]], " ", RowBox[List["Re", "[", SubscriptBox["zz", "2"], "]"]]]], "+", RowBox[List[RowBox[List["Im", "[", SubscriptBox["zz", "1"], "]"]], " ", RowBox[List["Im", "[", SubscriptBox["zz", "2"], "]"]]]]]], SuperscriptBox[RowBox[List["Abs", "[", SubscriptBox["zz", "2"], "]"]], "2"]]]]]]

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

2007-05-02