Complex arithmetic, holomorphy, power series, and harmonic functions.
Is it holomorphic?, tests for holomorphy and the standard obstructions.
Complex arithmetic and the logarithm, roots, branches, and branch points.
The Cauchy-Riemann equations, in rectangular, polar, and Wirtinger form.
Power series, the equivalence of holomorphy and analyticity, and Abel’s theorem.
Harmonic functions, real parts of holomorphic functions, and the mean value property.