Other
Imaginary Numbers Are Not Imaginary.
This site explores the concept of why imaginary numbers are not imaginary.
University of Toronto (Canada)
Do "Imaginary Numbers" Really Exist?
Contains a brief explanation of the existence of imaginary numbers.
Friesian School
Friesian.com: Imaginary Numbers
This site from Friesian.com contains a detailed definition of imaginary numbers along with a few examples.
Alabama Learning Exchange
Alex: Imaginary Numbers? What Do You Mean Imaginary?
Is it any wonder that students 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 the...
Mathigon
Mathigon: Real, Irrational, Imaginary Numbers
Explore this course in imaginary and complex numbers including topics of integers, real numbers, infinity, transcendental numbers, imaginary and complex numbers.
University of Toronto (Canada)
University of Toronto: Imaginary Numbers in Real World
This site from the University of Toronto contains revelant information regarding imaginary number appliances to the real world.
Khan Academy
Khan Academy: Simplify Roots of Negative Numbers
Rewrite square roots of negative numbers as imaginary numbers. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Oswego City School District
Regents Exam Prep Center: Simplifying Square Roots With Negative Numbers
This tutorial and practice shows how to simplify radicals even with a negative number. Features include a teacher page that has a Bingo game to teach the concept.
Khan Academy
Khan Academy: Simplify Roots of Negative Numbers
Rewrite square roots of negative numbers as imaginary numbers.
Math Open Reference
Math Open Reference: Root (Of a Number)
Learn how to find the root of a number. Topics covered include two roots, roots of negative numbers, and imaginary numbers. This site offers descriptions along with multiple examples.
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...
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,...
Math Open Reference
Math Open Reference: Imaginary Number
Learn about imaginary numbers with this handy reference guide. Provides a detailed definition and examples that enhance further explanation. Includes links to related topics.
Khan Academy
Khan Academy: Powers of the Imaginary Unit
Simplify expressions with base i (the imaginary unit) raised to a positive exponent. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Alabama Learning Exchange
Alex: Classifying Complex Numbers
This lesson helps young scholars distinguish between strictly complex numbers, strictly real numbers and strictly imaginary numbers while learning that real numbers and imaginary numbers are subsets of the set of complex numbers.
CK-12 Foundation
Ck 12: Quadratic Formula and Complex Sums
[Free Registration/Login may be required to access all resource tools.] Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms...
TED Talks
Ted: Ted Ed: Math Jokes Explained
It's not your typical knock-knock joke- these funny jests will tickle your imaginary numbers and teach you a thing or two about mathematics. [4:04]
Cut the Knot
Cut the Knot!: What Is a Number?
Casual and clear but definitely upper-level discussion of rational, real, imaginary, and several other types of numbers. Links to related sites.
Wolfram Research
Wolfram Math World: I
The imaginary number (also called the imaginary unit) is defined as the square root of negative one. This site explains the rational for the existence of the imaginary number "i" and gives formulas involving "i" including Euler's...
Oswego City School District
Regents Exam Prep Center: Cyclic Nature of the Powers of "I"
Students learn two easy methods to simplify "i" with any exponent. The practice page has several problems that include explanations. The teacher resource page has two possible activities for helping students understand the concept.
Math Is Fun
Math Is Fun: The Evolution of Numbers
Discusses what numbers are and how our understanding of them has evolved over thousands of years, from simple counting to negative numbers and irrational numbers, for example. Includes a set of practice questions where students identify...
Oswego City School District
Regents Exam Prep Center: Absolute Value of Complex Numbers
This tutorial presents the absolute value of complex numbers using formulas, graphs, and examples. There are practice problems and a teacher resource page to assist students in understanding the concept.
Cuemath
Cuemath: Complex Numbers
A comprehensive guide for learning all about complex numbers with definitions, operations on complex numbers, solved examples, and practice questions.
Clark University
Clark University: Dave's Short Trig Course: Complex Numbers: Absolute Value
Contains detailed information on absolute values for complex numbers.
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