CK-12 Foundation
Ck 12: Complex Numbers
[Free Registration/Login may be required to access all resource tools.] This lesson covers the powers of i, and adding and subtracting complex numbers, as well as how to plot them in the complex plane. Students examine guided notes,...
CK-12 Foundation
Ck 12: Complex Numbers
[Free Registration/Login may be required to access all resource tools.] A collection of resources that explain complex numbers and how to do arithmetic with them.
Interactive Mathematics
Interactive Mathematics: Polar Form of Complex Numbers
Using vectors as a starting point, this site demonstrates how complex numbers can be written in polar form. Several examples are included that require you to write complex numbers in polar and rectangular form and also represent them...
Interactive Mathematics
Interactive Mathematics: Complex Numbers: Basic Definitions
After reviewing the process of solving quadratic and cubic equations, a definition of an imaginary number is given. Also included is a demonstration of simplifying powers of the imaginary number and writing complex numbers. Examples are...
Interactive Mathematics
Interactive Mathematics: Basic Operations With Complex Numbers
Add, subtract, multiply and divide complex numbers using these easy-to-follow examples.
Alabama Learning Exchange
Alex: Imaginary Numbers? What Do You Mean Imaginary?
Is it any wonder that young scholars are suspicious? We lead, sometimes drag, them through Algebra I insisting they must follow the order of operations. We make them learn the "hard way" of doing an assignment one day only to show them...
Illustrative Mathematics
Illustrative Mathematics: Complex Distance
This problem is intended to reinforce the geometric interpretation of distance between complex numbers and midpoints as modulus of the difference and average respectively.
Math Open Reference
Math Open Reference: Complex Numbers
Explore complex numbers with this easy reference guide. Learn that complex numbers lie on a two-dimensional flat plane and have two components called the real and imaginary parts. Provides definitions and interactive activities that...
CK-12 Foundation
Ck 12: Precalculus Concepts 2.0
A complete high school Precalculus Concepts course. Includes 'Related Modalities' for each lesson that teach the same concept in different ways. The text materials follows Algebra II and comes before Calculus or Statistics. The content...
Shodor Education Foundation
Shodor Interactivate: Two Variable Function Pump
Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form.
Khan Academy
Khan Academy: Classify Complex Numbers
Classify numbers as real, pure imaginary, or complex.
Khan Academy
Khan Academy: Parts of Complex Numbers
Determine the real and the imaginary parts of complex numbers.
Khan Academy
Khan Academy: Add & Subtract Complex Numbers
Practice addition and subtraction with complex numbers.
Cuemath
Cuemath: Imaginary Numbers
In this instructional activity, you will learn about complex numbers and imaginary numbers. Included are solved examples and interactive questions for review.
CK-12 Foundation
Ck 12: 1.5 From Quadratics to Complex Numbers
This section introduces imaginary and complex numbers in the context of solutions to quadratic equations that don't have real-number solutions.
Khan Academy
Khan: Lesson 16: Part 2 Coordinate Geometry; Trigo and Radians; Complex Numbers
2 OF 2 FOR ADDITIONAL TOPICS IN MATH. Students will use the coordinate plane and equations of lines and circles to describe figures; create the equation of a circle given the figure or use the structure of a given equation to determine a...
Khan Academy
Khan Academy: Angle of Complex Numbers
Given a complex number of the form a+bi, find its angle.
Math Notes and Math Tests
Pre Calculus Notes: Complex Numbers [Pdf]
The resource discusses complex numbers. Topics examined are the complex plane, complex conjugates, dividing complex numbers, and complex zeros of functions.
Wolfram Research
Wolfram Math World: De Moivre's Identity
This MathWorld page states de Moivre's Identity.
University of Toronto (Canada)
How Can One Show That Imaginary Numbers Really Do Exist?
Contains a brief summary about the theory of imaginary numbers.
Windstream
Ojk's Precalculus Study Page: Geometric Representation of Complex Numbers
An introduction to viewing the complex plane in terms of polar coordinates. Assumes knowledge of the conversion formulas. Includes several examples and pictures.
Windstream
Ojk's Precalculus Study Page: Powers of Complex Numbers
An introduction to DeMoivre's Theorem for quickly finding the powers of complex numbers. Assumes knowledge of polar form of complex numbers. Includes several examples and pictures.
Richland Community College
Richland Community College: Math 116 Lecture Notes
This site from the Richland Community College provides the detailed lecture notes to a college algebra course, complete with equations and definitions. Content ranges from "functions and their graphs" to "conics and parametric equations."
Paul Dawkins
Paul's Online Notes: Algebra Cheat Sheet [Pdf]
An algebra "cheat sheet" to use as a reference when completing algebra homework. Lists basic facts, properties, operations, formulas, and functions, as well as common errors.