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.