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Upgrading from:

Graphics`ComplexMap`

The new two-parameter form of ParametricPlot now provides the functionality of Graphics`ComplexMap`.

CartesianMap functionality is now produced using ParametricPlot:

Version 5.2 << Graphics`ComplexMap`; CartesianMap[Exp, {-1, 1}, {-2, 2}]
Wolfram Language code: ParametricPlot[Through[{Re, Im}[Exp[x + I * y]]], {x, -1, 1}, {y, -2, 2}, PlotStyle -> None, Mesh -> 15]

PolarMap functionality is also produced using ParametricPlot:

Version 5.2 << Graphics`ComplexMap`; PolarMap[Sqrt, {0, 1} , {0, 2 Pi}]
Wolfram Language code: ParametricPlot[Through[{Re, Im}[Sqrt[r Exp[I t]]]], {r, 0, 1}, {t, 0, 2Pi}, PlotStyle -> None, Mesh -> 15]