Complex Maps

<<Graphics`ComplexMap`

SetOptions[Graphics,BaseStyle->{FontSize->20,FontWeight->"Bold"}];

Remove["Global`*"]

Conformal[mapType_,func_,xrange_,yrange_,options___]:=Framed[GraphicsArray[{mapType[#&,xrange,yrange,options],mapType[func,xrange,yrange,options]},ImageSize->500,PlotLabel->Style[func[z],Bold,16,FontFamily->"Helvetica"]]];
myf[z_]:=1/(z+1);

Conformal[CartesianMap,myf,{0.5,10,0.5},{-5,5,0.25},AxesLabel->{x,y},AxesOrigin->{0,0}]

myf[z_]:=(z-I)/(z+I);

Conformal[CartesianMap,myf,{-5,5},{0,5},Lines->30]

myf[z_]:=I*(1+z)/(1-z);

Options[Conformal]

Conformal[PolarMap,myf,{0,0.99},{0,2 Pi},Lines->20,PlotRange->{{-2,2},{-2,2}}]

myf[z_]:=(I*(1+z)/(1-z));
Conformal[PolarMap,myf,{0,0.99},{0,2 Pi},Lines->20,PlotRange->{{-2,2},{-2,2}}]
?Conformal