shape = Rectangle[{-1, -1}/2, {1, 1}/2]; rmf = RegionMember[shape]; f[z_] := z + 1 finverse[z_] := z - 1 ComplexRegionPlot[{rmf@ReIm@z, rmf@ReIm@finverse[z]}, {z, -2 - 2 I, 2 + 2 I}]