Topic: Radical Expressions

Subtopic: Complex Numbers

**Overview**

We finally get to work with imaginary numbers! So far we have been constrained in the Real realm, but today our world will open up to the Complex realm which includes imaginary numbers :) There is plenty of new terminology to learn, algebraic processes, and calculator processes.

Two cautions to take note of: (1) never leave i to a power, and (2) never leave i in the denominator of a fraction. Be sure you know how to simplify each of these cases.

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 10.7.1 Evaluate expressions involving square roots of negative numbers
- 10.7.2 Plot complex numbers on the complex plane
- 10.7.3 Simplify i to a power
- 10.7.4 Operations with complex numbers (algebraically and electronically) including adding, subtracting, multiplying, foiling, and dividing
- 10.7.5 Factor a sum of squares using imaginary numbers
- 10.7.6 Solve equations involving equivalent complex number

**Terminology**

Define: complex number system, non-real number, imaginary number, the basic imaginary number i, real part of a complex number, imaginary part of a complex number, conjugate of a complex number

**Supplementary Resources**

Read John and Betty's Journey Through Complex Numbers, an online story book about complex numbers. Particularly useful for this class are pages 14-21.

It is recommended that you be able to use a calculator (handheld or software) to do some of the processes covered in this lesson. If you have a handheld graphing calculator then these sites may help:

- For TI-84, TI-86, TI-89, or TI-92 see:

Prof. Keely's Calculator Guide: Complex Numbers

- For other models (or makes) try searching on one of the sites recommended here: FAQs - Graphing Calculator Tutorials