Agenda, Semester Week 3

Complex Numbers

Complex numbers and elementary complex functions are important tools for engineers for solving mathematical problems and describing physical systems. Of that reason we dedicate this week and a bit of next week to the study of complex numbers. We will begin by defining the complex numbers and showing notation and arithmetic tools for working with them. First and foremost it is important that you practice fundamental calculations with complex numbers until they feel no different than when working with the usual real numbers. Next, polar coordinates of a complex number will be introduced as well as trigonometric functions and their inverse functions, which are relevant in this context.

Key Terms

The set of complex numbers \(\mathbb C\). The elementary arithmetic operations on complex numbers: addition, subtraction, multiplication, and division. The imaginary unit \(i\). The rectangular form \(z=a+ib\), real part \(\mathrm{Re}\), and imaginary part \(\mathrm{Im}\). The complex conjugate \(\bar z\). Polar coordinates of complex numbers. Argument \(\mathrm{arg}\) and principal argument \(\mathrm{Arg}\). Modulus and the absolute value of complex numbers. Polar coordinates, the trigonometric functions, and the inverse trigonometric functions.

Preperation and Syllabus

This week will cover Sections 4.1 through 4.3 from Chapter 4 as well as the subsection about the inverse trigonometric functions in Section 2.2 from Chapter 2 in [the textbook].

Exercises

Exercises for Long Day.

Exercises for Short Day.