Purple Math
Purplemath: Complex Numbers: Introduction
This website provides an in-depth lesson on complex numbers. You learn about simplifying, adding, and multiplying complex numbers by viewing example problems that are worked through step-by-step. Continue on to pages 2 and 3 which...
Oswego City School District
Regents Exam Prep Center: Multiply and Divide Complex Numbers
This tutorial shows students how to multiply and divide complex numbers and includes the topic of conjugates. Includes link to a graphing calculator tutorial.
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: 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.
Clark University
Clark University: Dave's Short Trig Course: Complex Numbers
This site from a professor at Clark University teaches you about complex numbers.
OnlineMathLearning.com
Online Math Learning: Factor Polynomials With Complex Roots
A collection of video lessons with example problems and solutions to help students learn how to extend polynomial identities to the complex numbers. Includes interactive widget for working on the modeled problems or trying your own.
Illustrative Mathematics
Illustrative Mathematics: A sse.a.2 & N cn.a: Computations With Complex Numbers
This task requires learners to rewrite mathematical expressions involving complex numbers. Aligns with A-SSE.A.2 and N-CN.A.
Clark University
Clark University: Complex Numbers: The Complex Plane
A number of different ways to approach complex numbers and operations with them.
University College London
University College London: Complex Numbers: Real and Imaginary Parts
Contains a brief summary about the real and imaginary parts of complex numbers.
Khan Academy
Khan Academy: Multiply Complex Numbers (Basic)
Multiply complex numbers by single terms that are either real or imaginary. Students receive immediate feedback and have the opportunity to try questions repeatedly or receive hints.
Illustrative Mathematics
Illustrative Mathematics: N cn.a.2: Powers of a Complex Number
The goal of this task is to practice making calculations with complex numbers and to visualize what happens when two complex numbers are multiplied. Aligns with N-CN.A.2.
Math Medics
S.o.s. Math: The Complex Plane
Contains a lesson and practice exercises about complex numbers in a complex plane.
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...
Illustrative Mathematics
Illustrative Mathematics: N Cn, a Rei Complex Square Roots
Working with complex numbers allows us to solve equations that cannot be solved with real numbers. Here we will investigate complex numbers which arise as square roots of certain complex numbers. Aligns with N-CN.A.2 and A-REI.A.1.
CK-12 Foundation
Ck 12: Algebra Ii: 1.6 the Complex Plane
This section includes operations with imaginary and complex numbers and plotting numbers on the complex plane.
CK-12 Foundation
Ck 12: Plot Polar Coordinates
[Free Registration/Login may be required to access all resource tools.] Here you will learn how to convert and graph complex numbers in trigonometric or polar form using the polar coordinate system, which is similar in some ways to (x,...
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.
Other
Luis E. Romero: Solving Complex Problems With the 11 Laws of Systems Thinking
Systems thinking is the key to solving complex problems and achieving simplicity. Furthermore, by applying systems thinking to different situations, we also start to recognize the existence of universal patterns of behavior in business...
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.
Calculator Soup
Calculator Soup: Complex Fractions Calculator
A complex fraction is a fraction that contains another fraction. Use this Complex Fractions Calculator to do math and add, subtract, multiply and divide complex fractions. Fraction answers are provided in reduced form (lowest terms).
A&E Television
History.com: The World Trade Center, by the Numbers
When the World Trade Center's Twin Towers opened to the public in 1973, they were the tallest buildings in the world. Statistics: They rose a quarter-mile in the sky, contained 15 miles of elevator shafts, and nearly 44,000 windows. From...
Friesian School
Friesian.com: Imaginary Numbers
This site from Friesian.com contains a detailed definition of imaginary numbers along with a few examples.
New York Times
New York Times: Steven Strogatz on the Elements of Math Series the New York Times
[Free Registration/Login Required] On this site, Cornell University mathematics professor, Steven Strogatz, shares his 15-part series of columns on the elements of math. He investigates topics ranging from negative numbers to subtraction...
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.
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