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Unit: Complex numbers

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Possible mastery points

What are the imaginary numbers?

Learn
Intro to the imaginary numbers
(Opens a modal)
Intro to the imaginary numbers
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Powers of the imaginary unit
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Powers of the imaginary unit
(Opens a modal)
Simplifying roots of negative numbers
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i as the principal root of -1
(Opens a modal)
Practice
Powers of the imaginary unitGet 3 of 4 questions to level up!
Simplify roots of negative numbersGet 3 of 4 questions to level up!

What are the complex numbers?

Learn
Intro to complex numbers
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Intro to complex numbers
(Opens a modal)
Classifying complex numbers
(Opens a modal)
Practice
Parts of complex numbersGet 3 of 4 questions to level up!
Classify complex numbersGet 3 of 4 questions to level up!

The complex plane

Learn
Plotting numbers on the complex plane
(Opens a modal)
The complex plane
(Opens a modal)
Practice
Plot numbers on the complex planeGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 500 Mastery points

Adding and subtracting complex numbers

Learn
Adding complex numbers
(Opens a modal)
Subtracting complex numbers
(Opens a modal)
Practice
Add & subtract complex numbersGet 3 of 4 questions to level up!
Graphically add & subtract complex numbers Get 3 of 4 questions to level up!

Distance and midpoint of complex numbers

Learn
Distance & midpoint of complex numbers
(Opens a modal)
Practice
Distance of complex numbersGet 3 of 4 questions to level up!
Midpoint of complex numbersGet 3 of 4 questions to level up!

Quiz 2

Level up on the above skills and collect up to 400 Mastery points

Multiplying complex numbers

Learn
Multiplying complex numbers
(Opens a modal)
Multiplying complex numbers
(Opens a modal)
Complex number operations review
(Opens a modal)
Practice
Multiply complex numbers (basic)Get 3 of 4 questions to level up!
Multiply complex numbersGet 3 of 4 questions to level up!

Complex conjugates and dividing complex numbers

Learn
Intro to complex number conjugates
(Opens a modal)
Complex number conjugates
(Opens a modal)
Dividing complex numbers
(Opens a modal)
Dividing complex numbers review
(Opens a modal)
Practice
Complex number conjugatesGet 3 of 4 questions to level up!
Divide complex numbersGet 3 of 4 questions to level up!

Identities with complex numbers

Learn
Complex numbers & sum of squares factorization
(Opens a modal)
Factoring sum of squares
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Practice
Factor polynomials: complex numbersGet 3 of 4 questions to level up!

Quiz 3

Level up on the above skills and collect up to 500 Mastery points

Absolute value and angle of complex numbers

Learn
Absolute value of complex numbers
(Opens a modal)
Absolute value & angle of complex numbers
(Opens a modal)
Complex number absolute value & angle review
(Opens a modal)
Practice
Absolute value of complex numbersGet 3 of 4 questions to level up!
Angle of complex numbersGet 3 of 4 questions to level up!
Complex numbers from absolute value & angleGet 3 of 4 questions to level up!

Polar form of complex numbers

Learn
Polar & rectangular forms of complex numbers
(Opens a modal)
Complex number forms review
(Opens a modal)
Practice
Polar & rectangular forms of complex numbersGet 3 of 4 questions to level up!

Quiz 4

Level up on the above skills and collect up to 400 Mastery points

Multiplying and dividing complex numbers in polar form

Learn
Dividing complex numbers: polar & exponential form
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Visualizing complex number multiplication
(Opens a modal)
Powers of complex numbers
(Opens a modal)
Complex number equations: x³=1
(Opens a modal)
Visualizing complex number powers
(Opens a modal)
Complex number polar form review
(Opens a modal)
Practice
Multiply & divide complex numbers in polar formGet 3 of 4 questions to level up!
Powers of complex numbersGet 3 of 4 questions to level up!

Quiz 5

Level up on the above skills and collect up to 200 Mastery points
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Unit test

Level up on all the skills in this unit and collect up to 2000 Mastery points!

About this unit

In Algebra 2, students were introduced to the complex numbers and performed basic operations with them. In this unit, we extend this concept and perform more sophisticated operations, like dividing complex numbers. We also learn about a different way to represent complex numbers—polar form.