Module 1: Complex numbers and transformations

Topic A: Lessons 1-6: Complex numbers review

Learn

Lessons 1-3: No content yet
(Opens a modal)
Powers of the imaginary unit
(Opens a modal)
Powers of the imaginary unit
(Opens a modal)
Plotting numbers on the complex plane
(Opens a modal)
The complex plane
(Opens a modal)
Adding complex numbers
(Opens a modal)
Subtracting complex numbers
(Opens a modal)
Multiplying complex numbers
(Opens a modal)
Multiplying complex numbers
(Opens a modal)

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!

Topic A: Lessons 7-8: Complex number division

Learn

Intro to complex number conjugates
(Opens a modal)
Complex number conjugates
(Opens a modal)
Dividing complex numbers
(Opens a modal)

Practice

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

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

Learn

Lessons 9-10: No content yet
(Opens a modal)
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!

Topic B: Lesson 13: Trigonometry and complex numbers

Learn

Absolute value of complex numbers
(Opens a modal)
Absolute value & angle of complex numbers
(Opens a modal)
Polar & rectangular forms of complex numbers
(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 & rectangular forms of complex numbersGet 3 of 4 questions to level up!

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

Learn

Dividing complex numbers: polar & exponential form
(Opens a modal)
Visualizing complex number multiplication
(Opens a modal)

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

Powers of complex numbers
(Opens a modal)
Complex number equations: x³=1
(Opens a modal)
Visualizing complex number powers
(Opens a modal)

Practice

Powers of complex numbersGet 3 of 4 questions to level up!

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

Learn

Intro to matrices
(Opens a modal)
Intro to matrices
(Opens a modal)
Intro to matrix multiplication
(Opens a modal)
Multiplying matrices
(Opens a modal)
Multiplying matrices
(Opens a modal)
Transforming vectors using matrices
(Opens a modal)

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!
Transform vectors using matricesGet 3 of 4 questions to level up!

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

Learn

Transforming polygons using matrices
(Opens a modal)
Matrices as transformations
(Opens a modal)
Matrix from visual representation of transformation
(Opens a modal)
Visual representation of transformation from matrix
(Opens a modal)

Practice

Transform polygons using matricesGet 3 of 4 questions to level up!
Matrices as transformationsGet 3 of 4 questions to level up!

Topic C: Lesson 25: Properties of matrix addition

Learn

Adding & subtracting matrices
(Opens a modal)
Adding & subtracting matrices
(Opens a modal)
Multiplying matrices by scalars
(Opens a modal)
Multiplying matrices by scalars
(Opens a modal)
Intro to zero matrices
(Opens a modal)
Properties of matrix addition
(Opens a modal)
Properties of matrix scalar multiplication
(Opens a modal)

Practice

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

Topic C: Lesson 25: Properties of matrix multiplication

Learn

Intro to identity matrix
(Opens a modal)
Intro to identity matrices
(Opens a modal)
Dimensions of identity matrix
(Opens a modal)
Is matrix multiplication commutative?
(Opens a modal)
Associative property of matrix multiplication
(Opens a modal)
Zero matrix & matrix multiplication
(Opens a modal)
Properties of matrix multiplication
(Opens a modal)

Topic C: Lessons 26-30: Matrix inverses

Learn

Determinant of a 2x2 matrix
(Opens a modal)
Intro to matrix inverses
(Opens a modal)
Determining invertible matrices
(Opens a modal)
Finding inverse of a 2x2 matrix using determinant & adjugate
(Opens a modal)

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!

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