AnswersNC-Math 4 CRMultiply and Divide Complex Numbers

Multiply and Divide Complex Numbers Answers

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1
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The number 4 + i is multiplied by some real number to yield 2 + one-half i . Which equation is true?

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Option
Option A
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Option B
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Option C
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Option D
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Answer:

170186

3

Which description of the transformation of z on the complex plane gives the product of z = StartRoot 2 EndRoot (cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) ) and w = StartRoot 8 EndRoot (cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) ) ?

Question illustration
A
scale z by a factor of 4, then rotate counterclockwise radians
Option A
B
scale z by a factor of , then rotate counterclockwise radians
Option B
C
scale z by a factor of , and then rotate counterclockwise radians
Option C
D
scale z by a factor of 4, then rotate counterclockwise radians
Option D
4

Which description of the transformation of z on the complex plane gives the quotient of z = 8 (cosine (30 degrees) + i sine (30 degrees) ) and w = 2 (cosine (5 degrees) + i sine (5 degrees) ) ?

Question illustration
A
scale z by a factor of 2 and rotate it 5 degrees clockwise
Option A
B
scale z by a factor of and rotate it 5 degrees clockwise
Option B
C
scale z by a factor of 2 and rotate it 5 degrees counterclockwise
Option C
D
scale z by a factor of and rotate it 5 degrees counterclockwise
Option D
5

15 + 6i✔ 17 - i15 - 6i

A
15 + 6i
B
✔ 17 - i
C
15 - 6i
6

What is 3 [cos (60o )+ i sin 60o] • One-half [cos (15o) + i sin (15o)]?

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Option A
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Option B
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Option C
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Option D
7

4 - i4 + 2i17 + i17 - i

A
4 - i
B
4 + 2i
C
17 + i
D
17 - i
8

What is 6[cos(70°) + i sin(70°)] ÷ 2[cos(5°) + i sin(5°)]?

A
3[cos(75°) + i sin(75°)]
B
4[cos(75°) + i sin(75°)]
C
3[cos(65°) + i sin(65°)]
D
4[cos(65°) + i sin(65°)]
9

Let a = 3 – 5i and b = –1 + 7i. Which of the following are true statements? Check all that apply.ab = 38 + 16iab = 32 + 26i StartFraction a Over b EndFraction = negative StartFraction 19 minus 8 I Over 25 EndFraction ab = 2 + 2i StartFraction a Over b EndFraction = StartFraction 21 + 5 i Over 7 EndFraction StartFraction a Over b EndFraction = negative StartFraction 19 + 8 I Over 25 EndFraction

Question illustration
A
ab = 38 + 16i
B
ab = 32 + 26i
C
Option
Option C
D
ab = 2 + 2i
E
Option
Option E
F
Option
Option F
10

✔ 3 + i-3 + i-3 - i

A
✔ 3 + i
B
-3 + i
C
-3 - i

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