I would like to visualize the principal complex logarithm: $f(z)=Log(z)$. I have the following code
Table[ParametricPlot[
With[{z = u + I v}, {Re[Log[z]], Im[Log[z]]}], {u, -10, 10}, {v, n,
10}, PlotRange -> {{-2, 4}, {-0.5, 3.5}}, Mesh -> Automatic,
ImageSize -> 300], {n, 0.1, 1.6, 0.5}]
One can see that when the absolute value of the imaginary part is small, the result is far from precise. However, if plot only the image of a single line, it works perfectly well:
ParametricPlot[
With[{z = u + I 0.1}, {Re[Log[z]], Im[Log[z]]}], {u, -10, 10},
PlotRange -> {{-3, 4}, {-0.5, 3.5}}, Mesh -> Automatic,
ImageSize -> 300]
Is there a simple way to fix the first code?
PlotPoints
. TryPlotPoints -> 50
. $\endgroup$