Complex plane plots in Plots

The plots below are made using the defaults

default(linewidth=3, legend=false);

Point-based plots for complex arrays

Plots of Polar values are made on polar axes.

using ComplexPlots, Plots, ComplexValues
zc = cispi.(2*(0:400) / 400);
plot(@. Polar(0.5 + zc))

Plots of Spherical values are made on the Riemann sphere.

z = [complex(2cospi(t), 0.5sinpi(t)) for t in (0:400) / 200]
plot(Spherical.(z))

Function visualization

Plots of complex functions can be made using the zplot function. At each point in the complex domain, the hue is selected from a cyclic colormap using the phase of the function value, and the color value (similar to lightness) is chosen by the fractional part of the log of the function value's magnitude.

Examples:

default(aspect_ratio=1)
zplot(z -> (z^3 - 1) / (3im - z)^2)