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http://functions.wolfram.com/12.01.02.0003.01
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Abs[z] == Sqrt[Re[z]^2 + Im[z]^2]
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Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Equal]", SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["Re", "[", "z", "]"]], "2"], "+", SuperscriptBox[RowBox[List["Im", "[", "z", "]"]], "2"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ⩵ </mo> <msqrt> <mrow> <msup> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mrow> <mi> Im </mi> <mo> ⁡ </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>
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| 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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Date Added to functions.wolfram.com (modification date)
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){kind=small}
