Long division, synthetic division, rational functions and partial fractions decomposition included in the content as well. (0:00) Mathematica project ideas. (4:12) Preimages of rectangles under a mapping are regions between level curves of u and v. (14:36) Maximum principle for harmonic functions and an example over a disk, including optimization analysis along the boundary of the disk. (30:09) Polynomial roots and factorizations. (32:50) Example of a cubic with complex coefficients. Do polynomial long division and synthetic division if you are given one of the roots.
Based on "Fundamentals of Complex Analysis, with Applications to Engineering and Science", by E.B. Saff and A.D. Snider (3rd Edition). "Visual Complex Analysis", by Tristan Needham, is also referred to a lot. Mathematica is often used, especially to visualize complex analytic (conformal) mappings.