IntegerPart[z] == IntegerPart[Re[z]] + I IntegerPart[Im[z]]

Cell[BoxData[RowBox[List[RowBox[List["IntegerPart", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["IntegerPart", "[", RowBox[List["Re", "[", "z", "]"]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["IntegerPart", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> int </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mi> int </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mi> int </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> int </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <ci> int </ci> <apply> <real /> <ci> z </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <ci> int </ci> <apply> <imaginary /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["IntegerPart", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["IntegerPart", "[", RowBox[List["Re", "[", "z", "]"]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["IntegerPart", "[", RowBox[List["Im", "[", "z", "]"]], "]"]]]]]]]]]]

2001-10-29