Algebra Know-It-ALL

These worked-out solutions do not necessarily represent the only way a problem can be fig-

ured out. If you think you can solve a particular problem in a quicker or better way than you

see here, by all means go ahead! But always check your work to be sure your “alternative”

answer is correct.

Chapter 21

1. The 0th power of j is equal to 1. We know that j^2 =−1, so according to the difference
   of powers law,

j^0 =j^2 −^2

=j^2 /j^2

=−1/(−1)

= 1

2. We determined in this chapter that j^2 =−1,j^4 = 1, j^6 =−1,j^8 = 1, and so on for
   increasing even-integer powers of j. Based on this knowledge, we can use the negative
   powers rule to determine the following facts:

j−^2 = 1/(j^2 )

= 1/(−1)

=− 1

j−^4 = 1/(j^4 )

= 1/1

= 1

663

APPENDIX

C

Worked-Out Solutions to

Exercises: Chapters 21 to 29

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