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Course: Intermediate Algebra
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:

Terminology

Terms you should be able to 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 pages 13-22 of John and Betty's Journey Through Complex Numbers, an online story book about complex numbers.

Watch Imaginary Numbers are Real - Part 1: Introduction and Part 2: A Little History.

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:

rev. 2021-03-31