Complex analysis studies functions of a complex variable. It leans hard on a handful of facts about the numbers themselves. From College Algebra, you need i and arithmetic on a+bi. From Trigonometry, you need polar form, Euler's formula, De Moivre's theorem, and nth roots. From Calculus II, you need sequences, series, and power series. From Calculus III, you need partial derivatives, the Jacobian, and Green's theorem. This chapter works through each piece again in this course's own notation, so every tool is ready to use. It also points at exactly where the rest of this course is about to lean on it.
That forward-pointing is the whole point of reading this chapter closely. Chapter 1 turns "a complex number" into "a point in a plane." It asks what a set of such points can look like. Chapter 2 asks what a function of one complex number even means.
Chapter 3 asks what it means for such a function to be differentiable. It finds a far stronger condition than the real-variable one. The reason is that multiplication by a fixed complex number is always a rotation combined with a scaling. Raising a single number to a power shows the same pattern of turning and stretching.
By the time this course reaches Cauchy's theorem, Green's theorem from Calculus III will be doing real work inside its proof. By the time it reaches Liouville's theorem, it will use that result to give the Fundamental Theorem of Algebra a different proof from the one you saw in College Algebra.
Skim whatever already feels solid. Slow down wherever a review section surprises you. Nothing here is meant to take long. It is meant to make sure every tool is within reach the moment the next seven chapters reach for it.