# complex numbers

(1.4 hours to learn)

## Summary

Complex numbers are numbers expressible as a + bi, where i^2 = -1. They are often more convenient to work with than real numbers, because all complex (and hence all real) polynomials of degree n have n complex roots. Many trigonometric identities can be derived more simply using complex numbers.

## Context

-this concept has no prerequisites-

## Goals

- Be able to add, multiply, and divide complex numbers, and raise them to powers

- Know the definitions of
- complex conjugate
- norm (or absolute value) of a complex number

- Why can't i and -i be distinguished?

- Be able to work with the polar representation of complex numbers

## Core resources (read/watch one of the following)

## -Free-

→ Khan Academy: Algebra

## -Paid-

→ The Road to Reality (2007)

An overview of much of mathematical physics.

Location:
Chapter 4, "Magical complex numbers"

## Supplemental resources (the following are optional, but you may find them useful)

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 10.1, "Complex numbers," pages 493-498

## See also

-No Additional Notes-