(* uniforma_flow.nb *)

p=1;q=2;c=p-q I

Clear[f];f[z_]:=c z

phi[x_,y_]:=ComplexExpand[Re[f[x+I y]]]

psi[x_,y_]:=ComplexExpand[Im[f[x+I y]]]

(*次は1つずつ実行して式を見る*)

phi[x,y]

psi[x,y]

g1=ContourPlot[phi[x,y]==Table[level,{level,-5,5,1.0}],{x,-2,2},{y,-2,2},ContourStyle->Directive[Red,Thin]]

g2=ContourPlot[psi[x,y]==Table[level,{level,-5,5,1.0}],{x,-2,2},{y,-2,2},ContourStyle->Directive[Blue,Thin]]

vv[x_,y_]:={Re[f'[x+I y]],-Im[f'[x+I y]]}

g3=VectorPlot[vv[x,y],{x,-2,2},{y,-2,2},VectorScaling->Automatic]

gall=Show[g1,g2,g3]

Export["uniform_flow.png",gall]

Export["uniform_flow.pdf",gall]