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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.

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