This is a mini project that allows one to plot complex functions. The syntax is

import ComplexPlotting as CP
# Create meshgrids z_RE and z_IM, define a complex function.
CP.plot_complex(z_RE, z_IM, function(z_RE + 1j * z_IM))

One of the most straightforward examples is the square root, which has a branch cut in a certain direction on the complex plane (depending on your convention).

sqrt_z_I

The branch cut moves us to the second Riemann sheet, which is plotted below.

sqrt_z_II

Another interesting function is the logarithm.

log_z_I

Unlike the square root, logarithm has infinite amount of Riemann sheets, each obtained by adding/subtracting 2ドル\pi i$ sequentially.

log_z_II