I learned a lot about complex analysis today! Here's one way to visualize the function f(z) = 1/z, where z is a complex number. The height represents the real part of the result, while the hue represents the "angle" of the complex number.
This particular function has a "pole" at the origin, where it blows up to infinity. It's "simple" (has order 1), because it's "only" a 1/z blow-up. I think a 1/z^2 blow-up would have order 2?
#mathober2026 #math #complexanalysis
