Program, Semester Week 4

Complex Numbers and Polynomials

This week will start with a continued study of the complex numbers. In particular, the polar form of a complex number which uses the complex exponential function will be crucial for solving complex polynomial equations.

This leads us to the new topic of the week: the polynomials, which is an particularly important type of functions. We will study polynomials of various kinds and some of their key properties. Polynomials are functional expressions that will be useful for describing a vast amount of behaviour and trajectories, not least within the topic of kinematics in physics. Polynomials will appear in many connections in later courses, and will play a crucial role in later topics of our course..

Key Terms

Modulus \(\mathrm{mod}(z)\). Argument \(\mathrm{arg}(z)\) and principal argument \(\mathrm{Arg}(z)\). Polar form \(r\mathrm e^{\theta i}\). Polynomials, in particular second-degree polynomials. Polynomial equation. Root, real and imaginary. Polynomials with real coefficients. Binomials and the binomial equation.

Preperation and Syllabus

This week will cover Section 3.6 from Chapter [03 - Complex numbers] and Sections 4.1 through 4.4 from Chapter [04 - Polynomials].

Exercises

Exercises for Long Day.

Short day is dedicated to Theme Exercise 1. (See the description of Theme Exercises here. Theme Exercise 1 will be available via a link on the semester overview a few days before Short Day this week.)