Practice Workbook Answers (continued)

[Pages:12]Practice Workbook Answers (continued)

c. x2 17x 30 0 d. x2 3x 28 0

5. a. (x 2)Ax2 2x 4B b. (x 2)Ax2 2x 4B c. (5x 2)A25x2 10x 4B d. (5x 2)A25x2 10x 4B e. (x 6)Ax2 12B f. (2x 5)A4x2 12x 21B g. (x 2)3 h. (4x 3)Ax2 x 1B i. (y (2x 1))(y (2x 1)) Ay 2 (2x 1)2B j. Ax2 (y 2)B Ax2 (y 2)B k. A(y 2) zB AAy 2B 2 z(y 2) z2B l. (x 1)3

6. a. x 2 b. x2 4x 4 c. x3 6x2 12x 8 d. x4 8x3 24x2 32x 16 e. x5 10x4 40x3 80x2 80x 32

Lessons 2.14 and 2.15 Additional Practice

1. a. Ax2 5B Ax2 7B b. Ax3 4B2 c. Ax2 2B Ax4 2x2 4B d. Ax3 x2 xB2 e. AAx2 6) xB AAx2 6B xB f. Ax3 a3B2 a3x3 g. (x 2)Ax2 2x 4B(x 2) Ax2 2x 4B h. Ax4 8B Ax4 8B

2. a. Ax A4 "21BBAx A4 "21BB

b. 2Ax A1 "5BBAx A1 "5BB

3. a?c. Answers may vary. Samples: a. x2 6x 4 0 b. x2 6x 4 0 c. x4 16x2 4 0

4. a. x 121 c. x 55

b. x 123 d. x 3

5. a. x 2 b. x2 2x 4 c. x2 4 d. x4 2x3 4x2 8x 16 e. Ax2 2x 4B Ax2 2x 4B f. x4 16

g.

x6 1 4x3 1 16 (x 1 2)(x 2 2)

h.

(x 2

1

2)(x4 2 2x 1 4)(x4 (x 1 2)(x 2 2)

1

2x

1

4)

6.

g(x)

2x 3x

1 1

3 2

;

the

graphs

of

f (x)

and

g(x) are identical, except for a hole

discontinuity

at

Q 3,

9 11

R

in

the

graph

of f (x).

7. A 1; B 1

Chapter 3

Lessons 3.2 and 3.3 Additional Practice

1. a. none c. none e. none

b. x 1, 6 d. x 4 f. x 1

2. I. a. x 6, 1 c. none e. none

b. none d. x 4 f. none

II. a. none c. none e. none

b. none

d. none f. x 217

III. a. none

c.

x

27 4"73 2

e. x 4"3

b. none d. none f. none

IV. a?f. There are no nonreal solutions.

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Practice Workbook Answers (continued)

3. a. Yes; it simplifies to 10. b. No; it simplifies to 24 10"21. c. Yes; it simplifies to 1. d. Yes; it simplifies to 26.

4. a. 4 b. 3 e. 5 3"25

c. 8 d. 8 f. 6 "26

5. a. 12 7"21 c. 22 20"21

b. 8 39"21 d. 14 0"21

6. a. (x 3)Ax2 3x 9B

b.

x

3,

23

4 3"23 2

7. a. 27 c. "21 e. 45

b. "21 d. x2 4y 2 f. "21

Lessons 3.4 and 3.5 Additional Practice

1. a. 1

b. i

c. i

2. a. x 6 i c. x {5i

b. x 12 i d. z 2 { 3i

3. z 4 5i

4. a. any complex number where b 0 b. None exists; all rational numbers are real. c. any fraction with an integer numerator and denominator d. any complex number where a is rational and with b 0 e. None exists; all real numbers are complex, where b 0.

5. Solve x2 4 0 to get x 4"24, which simplifies to x {2i. Therefore, by factoring, x2 4 (x 2i)(x 2i).

6. a. 3 3i

c. 14 22i

e.

3 13

2 13

i

b. 4 9i

d.

2 5

1 5

i

f.

4 41

5 41

i

7. a. 1 c. 1 4i e. 49 20i g. 11 24i

b. 1 d. 1 4i f. 49 20i h. 11 24i

8.

a.

12 13

5 13

i

c.

x2 1 2xyi 2 y2 x2 1 y2

b.

23635

56 65

i

Lessons 3.7 and 3.8 Additional Practice

1. a?d.

5 3i

4i

2i

5 3i

4 2 2i

5 3i 4i

24 5 3i

2. a?d. 96i 84i

(3 i)4

72i

60i

48i

36i (3 i)3

24i

12i

(3 i)2

3i

6 12 18 24 30

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Practice Workbook Answers (continued)

3. a?b.

zz x yi

zz

x yi

c. Answers may vary. Sample: z, z, z z, and the origin form a parallelogram.

d. Answers may vary. Sample: z, z, z z, and the origin form a parallelogram.

4. a. x 3 or x 1

4i

2i

4 2 2i 4i

b. x 2 4i 2i

24

4 2 2i

4i

24

c. x 2 i or x 2 i 4i 2i

4

24

2i

4i

d. x 2 2i or x 2 2i 4i

2i

4 2 2i

4i

24

5. i

2 i 2 i 2i

3i

4

6

6 3i

6. a. "17 c. "442

b. "26 d. 10"10

7. 3 2i, 5, 6 i, 4 5i

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Practice Workbook Answers (continued)

8. a.

6i

w

zw

4i

2i

z 4 6 8 10 12 2i

zw 13 6i b.

zw 14i

12i

10i

8i

w

6i

4 2

zw 3 14i

c.

zw

6i

4i w

z4

2 zw 1 7i

z4

d.

2i z 4i

w 46

zw 10 5i e.

8 10 zw

6 4 2

z

4i

6i w

8i

10i

zw

12i

zw 6 12i f.

2i w zw

46 z 2i

zw 5

Lesson 3.9 Additional Practice

1. a. "41; ^ 38.7 b. "41; ^ 321.3 c. "41; ^ 141.3 d. "41; ^ 218.7

2. a. u z u 2"5; arg z ^ 63.43; b. u z u 2"5; arg z ^ 296.57; c. u z u 2"5; arg z ^ 116.57; d. u z u 2"5; arg z ^ 243.43;

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Practice Workbook Answers (continued)

3. a. u z 2 u 20; arg z2 ^ 126.86 b. u z 2 u 20; arg z2 ^ 233.14 c. u z 2 u 20; arg z2 ^ 233.14 d. u z 2 u 20; arg z2 ^ 126.86

4. a?b.

2i

z

2

2

2i

z

c. 2; 315

5. The magnitude doubles and the direction rotates 90 counterclockwise.

6. a. 0

b. ^ 18.43 c. ^ 36.86

d. ^ 53.13 e. ^ 71.57

7. a. i

1 z

1

1

z

i

1 z

1 2

1 2

i

b. 2i

1 z

2

1

z

2i

1 z

2 5

1 5

i

c. 2i

i

1 z

2 1

12

i

2i

z

1 z

2 7

"3 7

i

d.

i

z

1 z

1

2

3

i

1 z

3 10

1 10

i

8. a. u z u "10; u w u "17;

u zw u "170

b. u z u "10; u w u 2"5;

u zw u 10"2

c. u z u 4; u w u 5; u zw u 20

d.

uz

u

"10;

uw

u

"10 4

;

u

zw

u

10 4

2.5

Lesson 3.11 Additional Practice

1. a. 16; 120

b. 64; 180

c. x2 4x 16 0

2. IV

3. a. For z, take the square root of the

magnitude and half the direction of z2; for z3, cube the magnitude and triple the direction of z; for zn,

raise the magnitude of z to the nth

power, and multiply the direction

of z by n.

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Practice Workbook Answers (continued)

4. a. No, the magnitude is 9.

b. No, the magnitude could be any number from 0 to 6.

c. Yes, the magnitude is 3. d. No, the magnitude is 13. e. No, the magnitude is 9.

f. No, the magnitude is 6.

5. a.

4i 1 2i

4 3i

4 2 2i

4i

4 3 2i

b. 4i

2i

4 2 3i

4i

4 3 4i

c. 10i 8i

5 10i

4i 4 3i

4 2 2i

2 46 8i

d.

4i 1 3i

6 4i

2i

24 6

2i

5i

6. ^ 3"5 2"5 30; ^ 63 333 396

Lessons 3.12 and 3.13 Additional Practice

1. a. "10, ^ 18.4; 2"5, ^ 26.6 b. 10"2, ^ 45 c. 10, ^ 36.8; 20, ^ 53.2

2. a. (3 i)3 4(3 i)2 2(3 i) 20 0

b. 3 i, 2 c.

4i

2i

4 2 2i

4i

24

3. a. 1 b. 3i c. 1 2i d. 3 4i

4. x3 4x2 10x 40 0

5. 20 sides

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Practice Workbook Answers (continued)

6. a. 1, 30 c.

b. n 12 i

1

1

i

7. a. The magnitude of each solution is 1. The directions going counterclockwise are 60, 120, 180, 240, 300, and 360.

b.

{1,

{i,

{a

1 2

1

"3 2

b

,

{a

1 2

2

"3 2

b

8. i

1

1

i

Chapter 4

Lesson 4.2 Additional Practice

1. x 2, y 0 2. x 2, y 2, z 3 3. x 0, y 0, z 0 4. x 1, y 4, z 2, w 3

5. a. 2z 2w 3 2y 2w 1 2y 2z 0

b. 2z 2w 1 2y 2w 3 2y 2z 0

c. y 12, z 12, w 1 d. x 0, y 12, z 12, w 1

6. a 2, b 1, c 3

7. There is no solution to the system. The equations represent two lines that are parallel and therefore never intersect.

Lesson 4.3 Additional Practice

1. a21

22 21

`

28 27

b

a xy b

a223b

2. a223

2 2

`

6 6

b

a

x y

b

a

0 3

b

213 0x

2

3. ? 5 22 1 3 11? ? y ? ?21 ?

6 22 22 16 z

21

21 6 1 18 x

22

4. ? 1 23 22 3 216? ? y ? ? 2 ?

751

0z

4

5. 7, 3, and 11

6. 2x 3y 6z 5 x 3y z 0

6x 2y z 2

21

7.

?

1 3

3

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