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))
              

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Examples

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).

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

Another interesting function is the logarithm.

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