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http://functions.wolfram.com/04.06.27.0032.01
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Mod[m, n] == n (FractionalPart[m/n] + 1 + I) /; Re[m/n] < 0 && Im[m/n] < 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]], "\[Equal]", RowBox[List["n", RowBox[List["(", RowBox[List[RowBox[List["FractionalPart", "[", FractionBox["m", "n"], "]"]], "+", "1", "+", "\[ImaginaryI]"]], ")"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", FractionBox["m", "n"], "]"]], "<", "0"]], "\[And]", RowBox[List[RowBox[List["Im", "[", FractionBox["m", "n"], "]"]], "<", "0"]]]]]]]]
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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> <mrow> <mi> m </mi> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> FE`Conversion`Private`m </ci> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> <mo> ⩵ </mo> <mrow> <mi> n </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> frac </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> <mo> + </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> <mo> < </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mi> Im </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> <mo> ) </mo> </mrow> <mo> < </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <rem /> <ci> FE`Conversion`Private`m </ci> <ci> $CellContext`n </ci> </apply> <apply> <times /> <ci> n </ci> <apply> <plus /> <apply> <ci> FractionalPart </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> </apply> <apply> <and /> <apply> <lt /> <apply> <real /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <lt /> <apply> <imaginary /> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Mod", "[", RowBox[List["m_", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["FractionalPart", "[", FractionBox["m", "n"], "]"]], "+", "1", "+", "\[ImaginaryI]"]], ")"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", FractionBox["m", "n"], "]"]], "<", "0"]], "&&", RowBox[List[RowBox[List["Im", "[", FractionBox["m", "n"], "]"]], "<", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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