Table of Contents

Introduction to this Notebook

Introduction to complex numbers

How do imaginary numbers work?

Exploring powers of i

Complex numbers: real and imaginary parts

Adding and subtracting complex numbers

Multiplying complex numbers

Complex conjugates

Division of complex numbers

How to draw complex numbers

Adding using pictures

The polar form of complex numbers

The exponential form, rei q

De Moivre's theorem: raising a complex number to a power

Finding roots of a complex number

The position of roots on an Argand diagram

Expansion of sinnq and cosnq using De Moivre's theorem

The relationship between hyperbolic and trigonometric functions

Exit Quiz