Chapter 13

In This Chapter

Keeping an eye on the imaginary *i* and its powers

Operating on complex numbers: Addition, subtraction, and multiplication

Complex division: Multiplying by conjugates

Solving equations for complex solutions

The real numbers satisfied mathematicians and other scientists for centuries, but mathematicians eventually came across equations that couldn’t be solved and problems that couldn’t be answered without wandering into the realm of imaginary numbers.

*Imaginary numbers* involve the symbol *i*, which represents . Put imaginary numbers together with real numbers, and you get *complex* numbers. The complex number system consists of numbers of the form *a* + *bi*, with *a* and *b* representing real numbers.

In this chapter, you investigate the powers of *i*, perform operations on complex numbers, write the answers in the standard form, and finally, solve equations such as *x*^{2} = –16. Until the advent of imaginary numbers, equations such ...

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