Agenda, Semester Week 4

Complex Numbers and Polynomials

This week will continue our 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, a 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 many types of behaviour, 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 as well as in Mathematics 1b.

Key Terms

The polar form \(r\mathrm e^{\theta i}\) and the complex exponential function. Polynomials, in particular second-degree polynomials, and polynomial equations. Roots, real and imaginary. Polynomials with real coefficients. Binomials and the binomial equation.

Preperation and Syllabus

This week will cover Sections 4.4 through 4.6 from Chapter 4 and Sections 5.1 through 5.4 from Chapter 5 in [the textbook].

Exercises

Exercises for Long Day.

Exercises for Short Day.