Section 10.7 Complex Numbers
141.
2
44
23 62 3
ii iii
142. 11
12 12
ii
ii
112 112
12 12 12 12
ii ii
ii ii
143.
2
2
888
222
1
82 8(2)
22 (2)(2)
16 8 16 8( 1)
4(1)
4
16 8 8 16 8 16
41 5 5 5
ii
iii i
iiii
ii ii
ii i
i
iii
145.
111
xyz
2
()(3)(3)(3)
[3 6] [2(3) 3]
(3) [18 3]
315
gf g f
The solution set is
1
4, .
2
148.
2
2
9
90
(3)(3)0
x
x
xx
30 or 30
33
xx
xx
The solution set is
3, 3 .
Chapter 10 Radicals, Radical Functions, and Radical Exponents
Chapter 10 Review Exercises
1.
81 9
because
2
981
5.
5
32 2
because
5
232
6.
15 2 15 5 30 5
25 5
f
42458531.73f
55
2555
22
00
f
121525 3f
not a real number
8. To find the domain, set the radicand greater than or
equal to zero and solve the resulting inequality.
20
2
x
x
The domain of f is
2, .
10.
2
25 5xx
2
15.
5
5
32 7 2 7xx
16.
1
3
3
55xy xy
17.
333
2
16 16 4 64
18.
444
5
5
32 32 2 16
19.
1
2
77xx
22.
4
54
5
3
3x
xab
ab
4
5
3
x
ab
Chapter 10 Review Exercises
24.
111 32 1
223 66 6
1
3
5555
5
x
27.
1
912 912
33
11
912 34
33
xy xy
xy xy
30.
221
32332
2
42
4
43 1
6
66 6
xxx
xx
xxx
33. 37 21xy xy
34.
55
23
5
71177xx x
35.
45
666
55 5xx x
38.
86 6 26
33
66 2
3
3
22 2
54 27 2
27 2
32
xy x xy
xy x
xy x
41.
2435
33 3
332
3
33 2
3
2
3
44 16
82
82
22
xy xy xy
xyy
xy y
xy y
44.
33 3 3
63 23 6 2 3 83
Chapter 10 Radicals, Radical Functions, and Radical Exponents
45. 518 38 592 342
53 2 32 2
15 2 6 2
15 6 2 9 2
47.
33 33
33
33
33
26 548 26 586
26 526
26 106
210 6 86
49.
32
44
22
100 100
or
10 10
xxx
yy
xxx
x
yy
53.
477
45
42
42
44
444
64 64 32
2
2
16 2
16 2 2 2
xx
x
x
x
xx
xx xx
54.
32 32 5
2
2
42
200 200 100
2
2
100 10
xy xy xy
xy
xy
xxy x xy
56.
333 3 3
33
33
5 50 2 250 10
125 2 10
52 10
57.
735 765
58.
11 11
11 11 11
xy
xy x y
61.
22
713713
7137136
62.
2
2
735735 7 35
49 9 5
49 45 4
Chapter 10 Review Exercises
63.
4 4 64626
63
666
66.
22
510 10
22
55
55 5
yxyxy
xx
yy
yy y
68.
433
44
444
433
7773
333
3
x
xxxx
44
33 3
444
43
73 727
3
3
189
3
xx
x
x
x
x
71.
7753
53 5353
22
1025 32 1025 32
45 92
10 2 5 3 2
25 32 25 32
73.
22
553
333
3515
3
815
9
xxx
xxx
xxx
x
xx
x
Chapter 10 Radicals, Radical Functions, and Radical Exponents
76. 22222
777214
77.
322
33
33
322
333
22 2
33
333
3
33
39
xxx
yy x
xx
xy xy
79. 73
73
7373
7373
The solution set is
or .
82.
22
2
2
2
23 3
233
23 3
2396
0128
xx
xx
xx
xxx
xx
83.
415xx
22
45 1
45 1
xx
xx
Chapter 10 Review Exercises
85. a.
() 1.6 54fx x
(20) 1.6 20 54
46.8
f
In 2005 (20 years after 1985), 46.8% of
freshmen women described their health as above
average.; The rounded value is the same as the
value displayed by the graph.
86.
20,000 5000 100
20,000 5000 100
5000 5000
4100
x
x
x
91.
83 177 83 177
94
iiii
i
92.
2
43 2 43 42
12 8
12 1 8
12 8
ii ii i
ii
i
i
95.
2
2
78 78 7 8
49 64
49 64 1
49 64
ii i
i
Chapter 10 Radicals, Radical Functions, and Radical Exponents
97.
2
665306
55525
30 6 30 6
25 1 25 1
30 6 30 6
26 26 26
15 3
13 13
ii
iii i
ii
ii
i
99.
2
2
55 5
33 3
51
51
31 3
15 15
3333
iiiii
iii
i
ii
ii
Chapter 10 Test
1. a.
14 8 2 14
828 36 6
f
2.
4
3
444
3
3
1111
27 81
3
27
27
3.
1
1
11 1 1
2
8
24 2 4
1
1
84
25 25
5
xy xy
xy
6.
22
75 25 3 5 3xxx
7.
2
2
10 25 5
5
xx x
x
8.
48 3 6 2
33
16 8 2
xy x xy y
10.
322
3
3
510 50xyxy
3243
44 4
Chapter 10 Test
13.
33
46 3 6
33
2
33
23
88
2
2
xxy xxxy
xx y x
xy x
15.
34 6 5 34 6 3 5
418 15
492 15
432 15
12 2 15
18.
55 5xx
xx
xx
19.
33
22
3333
22233
55555
5555
xx
xxxx
33
525 25
5
xx
xx
2
2
23 69
0812
062
xxx
xx
xx
22
9422 7 7
92 7
92 7
94 7 3
12 4 7
37
xxx
xx
xx
xxx
x
x
33
3
11 6 3
11 6 3
11 6 27
11 33
3
x
x
x
x
x
The solution set is
3.
24.
40.4 2.9 20.1
x
Chapter 10 Radicals, Radical Functions, and Radical Exponents
25.
75 25 3 1
25 3 1 5 3i
28.
2
949141
9141
32 6 61
6 or 6 0
iii
i
30.
17
35 34 2
17
1
1
iiii i
i
ii
Cumulative Review Exercises (Chapters 1 – 10)
1.
2 5
23 6
xyz
xyz
236
2242
3 7 8
xyz
xyz
xz
6 12
2
z
z
Back-substitute –2 for z to find x.
34
xz
1
y
The solution is
2, 1, 2
or the solution set is
2, 1, 2 .
2.
2
2
3114
31140
31 40
xx
xx
xx
Apply the zero product principle.
310 40
xx
Cumulative Review
3.
24532
28536
2886
xxx
xxx
xx
4.
2
115 5
22
4
115 5
222 2
xx
x
xxx x
So that denominators will not equal zero, x cannot equal 2 or –2. To eliminate fractions, multiply by the
LCD,
22
xx
.
5.
22
211
21 1
21 1
xx
xx
xx
Chapter 10 Radicals, Radical Functions, and Radical Exponents
6.
22
24
xy
yx
First consider 22xy
. Replace the inequality
Now, use the origin as a test point.
020 2
02
This is a true statement. This means that the point
2
slope =
1
2
y–intercept = 2
Now, use the origin as a test point.
20 0 4
7.
2
2
2
840
lim
2
312
x
x
x
x
8.
11 1
11 1
xxxyxxy
xy
yy y
xy
yyxyyxy
xx x
10.
2
72
5
215
x
x
xx
72
53 5
23
7
53 53
x
xx x
x
x
xx xx
Cumulative Review
13.
32 32235
23 5 23 523 5
14.
2
32
32
2 5
22 3 3 4
24
xx
xxxx
xx
15.
23 52 3 42
23 8 6 5 6 202
636 40 3436
18. Since light varies inversely as the square of the
2
120 10
k
ld
k
are provided.
19. Let x = the amount invested at 7%.
Let y = the amount invested at 9%.
0.07 0.09 6000 510
0.07 540 0.09 510
540 0.02 510
0.02 30
1500
xx
xx
x
x
x