Agenda, Semester Week 3

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#

Long Day will cover:

  • The set of complex numbers \(\mathbb C\).

  • Elementary arithmetic operations on complex numbers: addition, subtraction, multiplication and division.

  • The imaginary unit \(i\).

  • Rectangular form: the real part \(\mathrm{Re}\) and imaginary part \(\mathrm{Im}\).

  • Complex conjugate \(\bar z\).

  • The absolute-value function in \(\mathbb C\).

Short Day will cover:

  • Polar coordinates of complex numbers: argument \(\mathrm{arg}\), principal argument \(\mathrm{Arg}\) and modulus \(\mathrm{mod}\).

  • Angles in radians

  • The fundamental trigonometric functions \(\cos,\sin,\tan\) and their inverses \(\arccos,\arcsin,\arctan\).

Preperation and Syllabus#

Syllabus this week is the first three sections of Chapter 4 and what we are missing from Chapter 2 (the subsections on trigonometric functions).

  • For Long Day, read Chapter 4 through Section 4.3 (you can leave out the parts from Section 4.3 about argument).

  • For Short Day, review Section 4.3 and read from after Example 2.3.2 onward in Chapter 2.

Exercises#

Exercises for Long Day.

Exercises for Short Day.

Contents