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# Module 1: Complex numbers and transformations

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Lessons 1-3: No content yetPowers of the imaginary unitPowers of the imaginary unitPlotting numbers on the complex planeThe complex planeAdding complex numbersSubtracting complex numbersMultiplying complex numbersMultiplying complex numbers

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!

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Intro to complex number conjugatesComplex number conjugatesDividing complex numbers

Practice

Complex number conjugatesGet 3 of 4 questions to level up!

Divide complex numbersGet 3 of 4 questions to level up!

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Lessons 9-10: No content yetDistance & midpoint of complex numbers

Practice

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

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

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Absolute value of complex numbersAbsolute value & angle of complex numbersPolar & rectangular forms of complex numbers

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!

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Dividing complex numbers: polar & exponential formVisualizing complex number multiplication

Practice

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

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Powers of complex numbersComplex number equations: x³=1Visualizing complex number powers

Practice

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

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Intro to matricesIntro to matricesIntro to matrix multiplicationMultiplying matricesMultiplying matricesTransforming vectors using matrices

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!

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Transforming polygons using matricesMatrices as transformationsMatrix from visual representation of transformationVisual representation of transformation from matrix

Practice

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

Matrices as transformationsGet 3 of 4 questions to level up!

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Adding & subtracting matricesAdding & subtracting matricesMultiplying matrices by scalarsMultiplying matrices by scalarsIntro to zero matricesProperties of matrix additionProperties of matrix scalar multiplication

Practice

Add & subtract matricesGet 3 of 4 questions to level up!

Multiply matrices by scalarsGet 3 of 4 questions to level up!

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Intro to identity matrixIntro to identity matricesDimensions of identity matrixIs matrix multiplication commutative?Associative property of matrix multiplicationZero matrix & matrix multiplicationProperties of matrix multiplication

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Determinant of a 2x2 matrixIntro to matrix inversesDetermining invertible matricesFinding inverse of a 2x2 matrix using determinant & adjugate

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!