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http://functions.wolfram.com/01.02.19.0023.01
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Abs[z^a] == E^Re[a Log[z]]
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Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", SuperscriptBox["z", "a"], "]"]], "\[Equal]", SuperscriptBox["\[ExponentialE]", RowBox[List["Re", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]]]]]
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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> <msup> <mi> z </mi> <mi> a </mi> </msup> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ⩵ </mo> <mrow> <mi> exp </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> </apply> <apply> <exp /> <apply> <real /> <apply> <times /> <ci> a </ci> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", SuperscriptBox["z_", "a_"], "]"]], "]"]], "\[RuleDelayed]", SuperscriptBox["\[ExponentialE]", RowBox[List["Re", "[", RowBox[List["a", " ", RowBox[List["Log", "[", "z", "]"]]]], "]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
