Algebra Know-It-ALL

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CHAPTER

30 Review Questions and Answers

Part Three

This is not a test! It’s a review of important general concepts you learned in the previous nine

chapters. Read it though slowly and let it “sink in.” If you’re confused about anything here, or

about anything in the section you’ve just finished, go back and study that material some more.

Chapter 21

Question 21-1

There are two distinct numbers that, when squared, produce −1. What are those two numbers?

Answer 21-1

One of them is the unit imaginary number, which we call j. That’s the engineer’s and applied

mathematician’s notation. Many mathematics texts use the letter i to represent it. The other is

the negative of the unit imaginary number, −j.

Question 21-2

How can we show that squaring −j produces the same result as squaring j?

Answer 21-2

By definition, we know that

j^2 =− 1

We can multiply the left side of this equation by (−1)^2 without having any effect on its value,

because (−1)^2 = 1. When we do that, we get

(−1)^2 j^2 =− 1

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