TITLE: What free tools can I use to plot complex functions on the complex plane?
QUESTION [9 upvotes]: I would like to plot $y = e^{ix}$ to view the imaginary unit circle and then change different parameters to see what happens. I am having trouble getting wolfram alpha to do this though. Is there a good way?

REPLY [2 votes]: cplot is a Python package I wrote. It uses  domain coloring and associates brightness to the modules of $f(z)$, and hue to its argument.
For the function $f(z) = z^6 + 1$:
import cplot

plt = cplot.plot(lambda z: z ** 6 + 1, (-1.5, +1.5, 400), (-1.5, +1.5, 400))
plt.show()