Here we shall see our first object from the realm of abstract algebra: a polynomial. Using polynomials, we shall also extend the field of real numbers to the field of complex numbers. We shall conclude the discussion with a geometric interpretation of these numbers.

1. Polynomial equations

2. Solvability of polynomial equations and the imaginary unit

3. The field of complex numbers

4. The fundamental theorem of algebra

5. Vieta's formulæ

6. Visualisation of complex numbers

7. Roots of unity