r=2
f[x_]:=Sqrt[1-x^2]
g[x_]:=1-x/r
h[x_]:=x*Tan[Pi/2-(Pi-2*ArcTan[r])]

Plot[{f[x],g[x],h[x]},{x,0,2}]

w[y_]:=Exp[y*(.1+I)]
ListLinePlot[Table[{Re[w[y]],Im[w[y]]},{y,-20,20,.01}]]