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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.
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Unit Plan
CK-12 Foundation

Ck 12: Quadratic Formula and Complex Sums

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

Ck 12: Polar Form of Complex Numbers

For Students 9th - 10th Standards
[Free Registration/Login may be required to access all resource tools.] Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for...
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Activity
Larson Texts

Larson Precalculus: Operations of Complex Numbers in the Complex Plane [Pdf]

For Students 9th - 10th Standards
A 3-page handout with examples and exercises in adding, subtracting, and multiplying complex numbers in the complex plane, as well as finding complex conjugates.
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Handout
Other

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.
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Interactive
Cool Math

Coolmath: What Are Complex Numbers?

For Students 9th - 10th Standards
Explanation and examples for complex numbers.
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eBook
Math Planet

Math Planet: Algebra 2: Complex Numbers

For Students 9th - 10th Standards
Provides an explanation, examples, and a video lesson all related to complex numbers.
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eBook
Mathigon

Mathigon: Real, Irrational, Imaginary Numbers

For Students 9th - 10th Standards
Explore this course in imaginary and complex numbers including topics of integers, real numbers, infinity, transcendental numbers, imaginary and complex numbers.
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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.
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Activity
Cool Math

Coolmath: Factoring Complex Numbers Exercises

For Students 6th - 9th Standards
This Algebra Cruncher generates an endless number of practice problems for factoring the sum of two squares. Each problem has hints and solutions.
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Lesson Plan
Illustrative Mathematics

Illustrative Mathematics: N cn.a.2: Powers of a Complex Number

For Teachers 9th - 10th Standards
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.
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Lesson Plan
Illustrative Mathematics

Illustrative Mathematics: N Cn, a Rei Complex Square Roots

For Teachers 9th - 10th Standards
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.
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Unknown Type
Khan Academy

Khan Academy: Graphically Add and Subtract Complex Numbers

For Students 9th - 10th Standards
Add or subtract complex numbers, and plot the result in the complex plane. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
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Unknown Type
Khan Academy

Khan Academy: Multiply Complex Numbers

For Students 9th - 10th Standards
Given two complex numbers, find their product. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
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Unknown Type
Khan Academy

Khan Academy: Multiply Complex Numbers (Basic)

For Students 9th - 10th Standards
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.
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Unknown Type
Khan Academy

Khan Academy: Divide Complex Numbers

For Students 9th - 10th Standards
Given a complex number division problem, express the result as a complex number of the form a+bi. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
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Unknown Type
Khan Academy

Khan Academy: Complex Number Conjugates

For Students 9th - 10th Standards
Given a complex number, find its conjugate or plot it in the complex plane. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
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Unknown Type
Khan Academy

Khan Academy: Angle of Complex Numbers

For Students 9th - 10th Standards
Given a complex number of the form a+bi, find its angle. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
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Handout
Lawrence Hall of Science

The Math Page: Skill in Algebra: Skill in Algebra: Complex or Imaginary Numbers

For Students 9th - 10th Standards
Clearly and thoroughly explains complex numbers. Provides example problems and exercises for students, with solutions available.
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Unit Plan
CK-12 Foundation

Ck 12: Analysis: Products and Quotients of Complex Numbers

For Students 11th - 12th Standards
[Free Registration/Login may be required to access all resource tools.] In this lesson, students calculate the products and quotients of complex numbers, identifying conjugates. Students examine guided notes, review guided practice,...
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Unit Plan
CK-12 Foundation

Ck 12: Polar Form of a Complex Number

For Students 11th - 12th Standards
[Free Registration/Login may be required to access all resource tools.] Here you will learn how to convert complex numbers from rectangular form to polar form. You will also explore the graphs of complex numbers on a polar graph.
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Unit Plan
CK-12 Foundation

Ck 12: Complex Numbers

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

Ck 12: Products and Quotients of Complex Numbers

For Students 9th - 10th Standards
[Free Registration/Login may be required to access all resource tools.] A collection of resources for learning about and practicing how to multiply and divide complex numbers.
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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.