Chapter 11

Plane Thinking: Complex Numbers and Polar Coordinates

In This Chapter

Pitting real versus imaginary

Exploring the complex number system

Plotting complex numbers on a plane

Picturing polar coordinates

Complex numbers and polar coordinates are some of the most interesting but often neglected topics in a standard pre-calculus course. Both of these concepts have very basic explanations, and they can vastly simplify a difficult problem or even allow you to solve a problem that you couldn’t solve before.

In previous math courses, you were told that you can’t find the square root of a negative number. If somewhere in your calculations you stumbled on an answer that required you to take the square root of a negative number, you simply threw that answer out the window. That changes here in Pre-Calculus For Dummies, however. As you advance in math, you need complex numbers to explain natural phenomena that real numbers are incapable of. In fact, entire math courses are dedicated to the study of complex numbers and their applications. We don’t go into that kind of depth here; we ...

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