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 Abs

 http://functions.wolfram.com/12.01.03.0004.01

 Input Form

 Abs[x + I y] == Sqrt[x^2 + y^2] /; Element[x, Reals] && Element[y, Reals]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["x", "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "\[Equal]", SqrtBox[RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]

 MathML Form

 "\[LeftBracketingBar]" x + y "\[RightBracketingBar]" x 2 + y 2 /; x TagBox["\[DoubleStruckCapitalR]", Function[Reals]] y TagBox["\[DoubleStruckCapitalR]", Function[Reals]] Condition x y x 2 y 2 1 2 x y [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", RowBox[List["x_", "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]]]], "/;", RowBox[List[RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["y", "\[Element]", "Reals"]]]]]]]]]]

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

 2001-10-29