If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Main content

Unit: Module 1: Complex numbers and transformations

0

Possible mastery points

Topic A: Lessons 1-6: Complex numbers review

Learn

Practice

Powers of the imaginary unitGet 3 of 4 questions to level up!
Plot numbers on the complex planeGet 3 of 4 questions to level up!
Add & subtract complex numbersGet 3 of 4 questions to level up!
Graphically add & subtract complex numbers Get 3 of 4 questions to level up!
Multiply complex numbers (basic)Get 3 of 4 questions to level up!
Multiply complex numbersGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 600 Mastery points

Topic A: Lessons 7-8: Complex number division

Learn

Practice

Complex number conjugatesGet 3 of 4 questions to level up!
Divide complex numbersGet 3 of 4 questions to level up!

Quiz 2

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

Topic B: Lessons 9-12: Distance and midpoint of complex numbers

Learn

Practice

Distance of complex numbersGet 3 of 4 questions to level up!
Midpoint of complex numbersGet 3 of 4 questions to level up!

Quiz 3

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

Topic B: Lesson 13: Trigonometry and complex numbers

Learn

Practice

Modulus (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 & 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

Topic B: Lessons 14-17: Multiplying and dividing complex numbers in polar form

Learn

Practice

Multiply & divide complex numbers in polar formGet 3 of 4 questions to level up!

Topic C: Lessons 18-19: Exploiting the connection to trigonometry

Learn

Practice

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

Topic C: Lessons 21-23: Transforming vectors with matrices

Learn

Practice

Matrix dimensionsGet 3 of 4 questions to level up!
Matrix elementsGet 3 of 4 questions to level up!
Multiply matricesGet 3 of 4 questions to level up!
Use matrices to transform 3D and 4D vectorsGet 3 of 4 questions to level up!

Quiz 6

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

Topic C: Lesson 24: Matrix notation encompasses new transformations!

Learn

Practice

Transform polygons using matricesGet 3 of 4 questions to level up!
Understand matrices as transformations of the planeGet 3 of 4 questions to level up!

Quiz 7

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

Topic C: Lesson 25: Properties of matrix addition

Learn

Practice

Add & subtract matricesGet 3 of 4 questions to level up!
Multiply matrices by scalarsGet 3 of 4 questions to level up!

Quiz 8

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

Topic C: Lesson 25: Properties of matrix multiplication

Learn

Topic C: Lessons 26-30: Matrix inverses

Learn

Practice

Determinant of a 2x2 matrixGet 3 of 4 questions to level up!
Determine inverse matricesGet 3 of 4 questions to level up!
Determine invertible matricesGet 3 of 4 questions to level up!
Find the inverse of a 2x2 matrixGet 3 of 4 questions to level up!

Up next for you:

Unit test

Level up on all the skills in this unit and collect up to 2800 Mastery points!

About this unit

"Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity. This leads to the study of complex numbers and linear transformations in the complex plane. The teacher materials consist of the teacher pages including exit tickets, exit ticket solutions, and all student materials with solutions for each lesson in Module 1." Eureka Math/EngageNY (c) 2015 GreatMinds.org