after plotting this function:
ParametricPlot[
With[{z = Exp[I θ]},
Through[{Re, Im}[
1 - ((I 0.8) Log[(1 - E^(-((I π 0.2)/0.8)) z)/(1 - E^((I π 0.2)/0.8) z)])/π
]] ],
{θ, 0, 2 π}, ImageSize -> Medium, PlotRange -> {{-1, 1}, {-1, 1}}]
Or alternatively, after substituting in the value for z
outside the plotting function:
ParametricPlot[{1 +
Re[(0.` - 0.25464790894703254` I) Log[(
1 - (0.7071067811865476` - 0.7071067811865475` I) E^(I θ))/(
1 - (0.7071067811865476` + 0.7071067811865475` I) E^(I θ))]],
Im[(0.` - 0.25464790894703254` I) Log[(
1 - (0.7071067811865476` - 0.7071067811865475` I) E^(I θ))/(
1 - (0.7071067811865476` + 0.7071067811865475` I) E^(I θ))]]}, {θ, 0, 2 π},
ImageSize -> Medium, PlotRange -> {{-1, 1}, {-1, 1}}]
I don't know what should I add to make something as a shadow to the resulting line to separate the two resulting plans. Does anyone have any suggestions?