Sample Mathematica file.

<< complex.m
f[z_] := z^2;
f1 = CartesianMap[f,{0,2,.2},{-4,4,.2},
     DefaultFont -> {"HelveticaBold",16},
     AxesStyle -> Thickness[.005],
     Ticks ->{{-16,-12,-8,-4,4},
     {-16,-12,-8,-4,4,8,12,16}}];
f2 = CartesianMap[f,{0,4,.2},{-2,2,.2},
     DefaultFont -> {"HelveticaBold",16},
     AxesStyle -> Thickness[.005],
     Ticks ->{{-16,-12,-8,-4,4,8,12,16},
     {-16,-12,-8,-4,4}}];
     
Show[f1,f2,Ticks ->{{-16,-12,-8,-4,4,8,12,16},
     {-16,-12,-8,-4,4,8,12,16}}];

PolarMap[f,{2,.2},{-Pi/2+Pi/24,Pi/2-Pi/24,Pi/24}]