Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Intermediate Algebra
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

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.

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