Algebra Know-It-ALL

absolute values equal to k. These are shown as points in Fig. C-1. There are infinitely

many complex numbers with absolute values equal to k. This fact can be shown in the

complex-number plane by plotting the set of all points at a distance of k units from the

origin. This set of points forms a circle with radius k.

Chapter 22

1. To multiply out this equation, we must apply the product of sums rule on the left side
   of the equals sign. To keep the signs right, let’s change the subtraction into a negative
   addition before we start multiplying, and then change the negative additions back to
   subtractions when we’re done. Here are the steps:

(− 7 x− 5)(− 2 x+ 9) = 0

[− 7 x+ (−5)](− 2 x+ 9) = 0

(− 7 x)× (− 2 x)+ (− 7 x)× 9 + (−5)× (− 2 x)+ (−5)× 9 = 0

14 x^2 + (− 63 x)+ 10 x+ (−45)= 0

14 x^2 + (− 53 x)+ (−45)= 0

14 x^2 − 53 x− 45 = 0

a

jb

Radius of

circle

=kunits

(0,-k)

or

• j

j

k

(0,k)

or

j

j

k

(k,0)

or

k

(-k,0)

or

• k

Figure C-1 Illustration for the solution to Prob. 10 in

Chap. 21.

Chapter 22 669