TITLE: How to plot complex functions on the paper by your hand?
QUESTION [5 upvotes]: I want to know the exact method of plotting complex function used by human, computer, and whatever who can do mathematics.
For example how should I plot this : $w = u+iv$ , $z = x+iy$ , $w= f(z)= z^2$
I'm completely confused imagining the complex functions and I want to know how you would imagine such functions and do mathematics with it.
Thanks in advance

REPLY [2 votes]: I just wanted to point out that I wrote a Python package, cplot, that makes plotting complex-valued functions fairly simple.
It combines domain coloring and contour lines for constant arg/abs.
e.g., for $\sin(z)/z$:
import cplot
import numpy as np


def f(z):
    return np.sin(z) / z


plt = cplot.plot(f, (-7.0, +7.0, 400), (-7.0, +7.0, 400))
plt.show()