# Complex Numbers

### Introduction and Summary

Until now, we have been dealing exclusively with real numbers. This chapter introduces a new topic--imaginary and complex numbers. Complex numbers are numbers of the form a + bi , where i = and a and b are real numbers. They are used in a variety of computations and situations. Complex numbers are useful for our purposes because they allow us to take the square root of a negative number and to calculate imaginary roots.

The first section discusses i and imaginary numbers of the form ki . Here, the reader will learn how to simplify the square root of a negative number.

The focus of the next two sections is computation with complex numbers. Section two explains how to add and subtract complex numbers, how to multiply a complex number by a scalar, and how to multiply a complex number by another complex number. Section three introduces the concept of a complex conjugate and explains its use in dividing a complex number by another complex number.

Complex numbers are useful in a variety of situations. They appear frequently in almost every branch of mathematics. We will use them in the next chapter when we find the roots of certain polynomials--many polynomials have zeros that are complex numbers.

## Take a Study Break

### Star Trek gets SEXY

Chris Pine and Zoe Saldana heat up the red carpet!

### Are you afraid of relationships?

Auntie SparkNotes can help!

### Sexy starlet style

See every single look from the Met Gala!

### Geeky Actors: Then and Now

Travel back in time!

### 10 Movies Better Than Their Books

What do you think?

### How To Look Like J-Law...

When you don't look like J-Law.

### 12 Scientific Inaccuracies in Into Darkness

What did Star Trek get wrong?

### Villains We Want These Actresses to Play

From super cute to super bad!

## The Book

### Read What You Love, Anywhere You Like

Get Our FREE NOOK Reading Apps