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Mathematica Notation

Traditional Notation

Complex Components > Abs[z] > Representations through equivalent functions > With related functions > With Im




Input Form

Abs[z] == Sqrt[Re[z]^2 + Im[z]^2]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Equal]", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["Re", "[", "z", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Im", "[", "z", "]"]], "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> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> z </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#10869; </mo> <msqrt> <mrow> <msup> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <ci> z </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <imaginary /> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["Re", "[", "z", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Im", "[", "z", "]"]], "2"]]]]]]]]

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