Rouché's theorem and applications to polynomials. Online lectures for Complex Analysis I at Oklahoma State University.
There are two typos:
In the proof of the theorem, you need to replace g by -g, but that does not change the conclusion.
In one of the examples, it should be z^n + 1, not z^n - 1.
See https://www.jirka.org/ca/ for the (free online) book "Guide to Cultivating Complex Analysis" these lectures are based on.
