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Complex numbers

The imaginary unit i

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

Complex numbers introduction

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Intro to complex numbers
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Intro to complex numbers
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Classifying complex numbers
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Parts of complex numbersGet 3 of 4 questions to level up!
Classify complex numbersGet 3 of 4 questions to level up!

The complex plane

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Plotting numbers on the complex plane
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The complex plane
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Practice
Plot numbers on the complex planeGet 3 of 4 questions to level up!

Adding & subtracting complex numbers

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Adding complex numbers
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Subtracting complex numbers
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Practice
Add & subtract complex numbersGet 3 of 4 questions to level up!

Multiplying complex numbers

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

Quadratic equations with complex solutions

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Solving quadratic equations: complex roots
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Solve quadratic equations: complex solutionsGet 3 of 4 questions to level up!

About this unit

Complex numbers are built on the idea that we can define the number i (called "the imaginary unit") to be the principal square root of -1, or a solution to the equation x²=-1. From this starting point evolves a rich and exciting world of the number system that encapsulates everything we have known before: integers, rational, and real numbers.