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Mrao: Imaginary Numbers Are Not Real

For Students 9th - 10th Standards
This site presents a tutorial introduction to the ideas of geometric algebra. Gives an outline of geometric algebra and discusses the geometric product, imaginary numbers, and more.
Handout
Math Warehouse

Math Warehouse: Complex and Imaginary Numbers

For Students 9th - 10th Standards
Features numerous exercises relating to complex and imaginary numbers. Includes video tutorials, calculators, worksheets and more.
Handout
University of Toronto (Canada)

How Can One Show That Imaginary Numbers Really Do Exist?

For Students 9th - 10th Standards
Contains a brief summary about the theory of imaginary numbers.
Handout
National Council of Teachers of Mathematics

The Math Forum: Drexel University Math Forum: Imaginary Numbers

For Students 9th - 10th Standards
Contains a short summary on imaginary numbers and several links to its related fields. Also provides several examples and explanations for understanding.
Unit Plan
CK-12 Foundation

Ck 12: Analysis: Imaginary Numbers

For Students 10th - 12th Standards
[Free Registration/Login may be required to access all resource tools.] In this lesson students will identify imaginary and complex numbers, basic evaluation of imaginary numbers. Students examine guided notes, review guided practice,...
Unit Plan
Khan Academy

Khan Academy: Simplify Roots of Negative Numbers

For Students 9th - 10th Standards
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.
Activity
University of Toronto (Canada)

Do "Imaginary Numbers" Really Exist?

For Students 9th - 10th Standards
Contains a brief explanation of the existence of imaginary numbers.
Unit Plan
CK-12 Foundation

Ck 12: Imaginary Numbers

For Students 9th - 10th Standards
[Free Registration/Login may be required to access all resource tools.] Know there is a complex number i such that i squared = -1, and every complex number has the form a + bi with a and b real.
Activity
Oswego City School District

Regents Exam Prep Center: Absolute Value of Complex Numbers

For Students 9th - 10th Standards
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.
Lesson Plan
Alabama Learning Exchange

Alex: Imaginary Numbers? What Do You Mean Imaginary?

For Teachers 9th - 10th
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...
Activity
Oswego City School District

Regents Exam Prep Center: Simplifying Square Roots With Negative Numbers

For Students 9th - 10th
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.
Handout
Free Math Help

Free Math Help: Imaginary Numbers

For Students 9th - 10th Standards
The lesson investigates imaginary numbers. An explanation and sample exercises are provided.
Unit Plan
Khan Academy

Khan Academy: Powers of the Imaginary Unit

For Students 9th - 10th Standards
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.
Unit Plan
CK-12 Foundation

Ck 12: Complex Numbers

For Students 9th - 10th Standards
[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.
Unit Plan
Oswego City School District

Regents Exam Prep Center: Complex Numbers

For Teachers 9th - 10th Standards
A wealth of material to help you plan classroom instruction on complex numbers: several lessons that cover the number i, square roots of negative numbers, and operations involving complex numbers; practice activities, some of which...
Handout
Wolfram Research

Wolfram Math World: Imaginary Number

For Students 9th - 10th Standards
Contains a brief definition of an imaginary number. Includes special links and topic search engine.
Activity
Math Medics

S.o.s. Math: The Complex Numbers

For Students 9th - 10th Standards
This lesson may be useful to both persons with prior knowledge of complex numbers and those without. The lesson begins with the definition of complex numbers and its notation, then gives the rules of arithmetic for them with exercises....
Unit Plan
CK-12 Foundation

Ck 12: Analysis: Products and Quotients of Complex Numbers

For Students 10th - 12th Standards
[Free Registration/Login may be required to access all resource tools.] This lesson covers multiplying and dividing complex numbers. Students examine guided notes, review guided practice, watch instructional videos and attempt practice...
Unit Plan
Interactive Mathematics

Interactive Mathematics: Complex Numbers

For Students 9th - 10th Standards
The world of complex numbers is explored through mini lessons, interactive examples, applications and demonstrations. Topics covered include definitions, basic operations, graphing, different forms of complex numbers, products,...
Handout
Wolfram Research

Wolfram Math World: I

For Students 9th - 10th
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...
Handout
Math Words

Math words.com: Complex Numbers

For Students 9th - 10th Standards
At MathWords.com, a definition is given for what complex numbers are, along with some examples.
Unit Plan
Khan Academy

Khan Academy: Powers of Complex Numbers

For Students 9th - 10th Standards
Simplify a power of a complex number z^n, or solve an equation of the form z^n=k. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Handout
University of Toronto (Canada)

The Origin of Complex Numbers and the Notation "I"

For Students 9th - 10th Standards
Contains a brief summary on the origin of complex numbers.
Activity
Oswego City School District

Regents Exam Prep Center: Cyclic Nature of the Powers of "I"

For Students 9th - 10th
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.

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