Intermediate Algebra (11th edition)

Multiply or divide as indicated. See Examples 2 and 3.

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19. 20. 21. 22.

23. 24. 25. 26.

27.Every real number is a complex number. Explain why this is so.

28.Not every complex number is a real number. Give an example, and explain why this state-

ment is true.

Add or subtract as indicated. Write your answers in the form. See Examples 4 and 5.

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41.Concept Check Fill in the blank with the correct response:

Because using the definition of subtraction, we can check

this to find that.

42.Concept Check Fill in the blank with the correct response:

Because using the definition of division, we can check this to find that

.

Multiply. See Example 6.

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61.Concept Check What is the conjugate of

62.Concept Check If we multiply by its conjugate, we get ,

which is always a real number.

Find each quotient. See Example 7.

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67. 68. 69. 70.

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5 +i

• i

3 - i

• i

5 - i

i

3 +i

i

• 1 + 5 i
  3 + 2 i

2 - 3 i

2 + 3 i

• 38 - 8 i
  7 + 3 i


• 7 + 4 i
  3 + 2 i


• 8 i
  1 +i

8 i

2 + 2 i

2

1 +i

2

1 - i

a+bi

a+bi?

17 + 2 i 217 - 2 i 2 11 +i 2211 - i 22 12 - i 2212 +i 22

112 + 3 i 2112 - 3 i 2 16 + 7 i 216 - 7 i 2 14 + 9 i 214 - 9 i 2

13 + 2 i 22 2 i 1 - 4 - i 22 3 i 1 - 3 - i 22

14 + 3 i 211 - 2 i 2 17 - 2 i 213 +i 2 14 + 5 i 22

1 - 32 i 21 - 2 i 2 5 i 1 - 6 + 2 i 2 3 i 14 + 9 i 2

13 i 2127 i 2 15 i 21125 i 2 1 - 8 i 21 - 2 i 2

1 - 2 - i 212 - i 2 =

• 5
  2 - i=-^2 - i,

11 +i 2 + 13 +i 2 =

14 + 2 i 2 - 13 +i 2 = 1 +i,

317 + 3 i 2 - 14 - 2 i 24 + 13 +i 2 317 + 2 i 2 + 1 - 4 - i 24 - 12 + 5 i 2

1 - 4 + 11 i 2 + 1 - 2 - 4 i 2 + 17 + 6 i 2 1 - 1 +i 2 + 12 + 5 i 2 + 13 + 2 i 2

1 - 3 - 4 i 2 - 1 - 1 - 4 i 2 1 - 2 - 3 i 2 - 1 - 5 - 3 i 2

14 +i 2 - 1 - 3 - 2 i 2 19 +i 2 - 13 + 2 i 2

15 - i 2 + 1 - 5 +i 2 1 - 2 + 6 i 2 + 12 - 6 i 2

13 + 2 i 2 + 1 - 4 + 5 i 2 17 + 15 i 2 + 1 - 11 + 14 i 2

a+bi

- - 100

- 25

- - 64

- 16

- 160

 10

- 75

 3

- 40

- 10

- 300

- 100

- 3 # 11 - 10 # 2

- 7 #- 15 - 3 #- 19 - 4 #- 25 - 9 #- 81

480 CHAPTER 8 Roots, Radicals, and Root Functions