Fearless Symmetry 5/23: Complex Numbers

I read the fifth chapter of Fearless Symmetry.

Part 1: Algebraic Preliminaries

Chapter 5: Complex Numbers

Well, I think it is safe to assume that readers of this blog know the complex numbers. This chapter is in fact about a subset of the Complex Numbers called the Algebraic Numbers. In FS they use $\mathbf{Q}^{Alg}$ as notation, whereas I have seen mostly the notation $A$ for the Algebraic Numbers.

Every algebraic number can be expressed as the root of of a polynomial equation with integer coefficients. So $\pi$ is not a member of $\mathbf{Q}^{Alg}$, but $\sqrt{2}$ is because $\sqrt{2}$ is a solution of $x^2 - 2 = 0$.

Visualisation of the (countable) field of algebraic numbers in the complex plane.
( From Wikipedia )

To be continued with 6. Equations and varieties