AnswersNC-Math 4 CRMultiply and Divide Complex Numbers

Multiply and Divide Complex Numbers — Unit test Answers

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What is the quotient of ?

Question illustration
A
45 (cosine (StartFraction pi Over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
Option A
B
88 (cosine (StartFraction pi Over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
Option B
C
45 (cosine (StartFraction pi Over 6 EndFraction) + I sine (StartFraction pi Over 6 EndFraction) )
Option C
D
88 (cosine (StartFraction pi Over 6 EndFraction) + I sine (StartFraction pi Over 6 EndFraction) )
Option D
2
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Based on the sketch below, how far is Joey’s house from the park?

Question illustration
A
0.74 mi.
B
0.86 mi.
C
2.21 mi.
D
2.35 mi.
3

Jake and Maddie each take the closest path from their homes to the store. Based on the picture below, what is the approximate difference in the distance each person traveled to the store?

Question illustration
A
1.4 m
B
5.9 m
C
6.4 m
D
7.7 m
4

For two complex numbers z and w, which diagram shows the geometric representation of zw?

A
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line with length r 1 goes to point z, a line with length r 1 + r 2 goes to point z w, and a line with length r 2 goes to point w. The angle to line w is theta 2, z is theta 1, z w is theta 1 minus theta 2.
Option A
B
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line with length r 1 goes to point z, a line with length r 1 r 2 goes to point z w, and a line with length r 2 goes to point w. The angle to line w is theta 2, z is theta 1, z w is theta 1 minus theta 2.
Option B
C
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line with length r 1 + r 2 goes to point z w, a line with length r 1 goes to point z, and a line with length r 2 goes to point w. The angle to line w is theta 2, z is theta 1, z w is theta 1 + theta 2.
Option C
D
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line with length r 1 r 2 goes to point z w, a line with length r 1 goes to point z, and a line with length r 2 goes to point w. The angle to line w is theta 2, z is theta 1, z w is theta 1 + theta 2.
Option D
5

Review the graph.

Question illustration
A
quadrant I
B
quadrant II
C
quadrant III
D
quadrant IV
6

A tree is growing on a hill. In an attempt to make the tree grow straight up, a 12-foot-long wire is attached to a tree at a point 6 feet off the ground. The wire is anchored to the ground 10 feet from the base of the tree. At what angle is the tree growing in relation to the hill?

Question illustration
A
82.3°
B
88.1°
C
93.8°
D
128.0°
7

What are the solutions to the equation over the interval [0, 2]?

Question illustration
A
only
Option A
B
only
Option B
C
only
Option C
D
StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 7 pi Over 6 EndFraction and StartFraction 11 pi Over 6 EndFraction
Option D
8

Which number represents the sum of –8 and –i?

A
8i
B
–8i
C
–8 – i
D
–8 + i
9

Which pair of complex numbers has a real-number product?

A
(1 + 3i)(6i)
B
(1 + 3i)(2 – 3i)
C
(1 + 3i)(1 – 3i)
D
(1 + 3i)(3i)
10

Which equation is an example of the commutative property of multiplication?

A
(4 + 2i) = (2i + 4)
B
(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)
C
(4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)(1)
D
(4 + 2i) = (4 + 2i + 0)
11

The bottom of a 12-foot ladder is placed on the ground 7 feet from the base of a pipe sticking out of the ground. The top of the ladder is placed an unknown distance off the ground, leaning on the pipe. The ladder and the ground meet at a 56.4° angle. At what angle does the pipe meet the ground?

A
35.7°
B
46.7°
C
55.7°
D
88.2°
12

Given z1 = 2 + and z2 = 1 – , what is the sum of z1 and z2?

Question illustration
A
1
B
3
C
3 + 2
Option C
D
–1 – 2
Option D
13

Jamal draws triangle XYZ. If what is the approximate length of XY?

Question illustration
A
3.4 or 10.4
B
6.4 or 13.7
C
10.4
D
13.7
14

From where Kiana is standing, she must look up at a 50° angle to see the top of a building. If she backs up 50 feet, she will need to look up at a 40° angle to see the top of the same building. Approximately how tall is the building?

Question illustration
A
119.0 ft.
B
141.8 ft.
C
185.1 ft.
D
220.6 ft.
15

What is one possible solution for the triangle below?

Question illustration
A
Y Z similar to 43 point 0, m angle X similar to 94 point 6 degree, m angle Z similar to 17 point 4 degree.
Option A
B
Y Z similar to 19 point 3, m angle X similar to 85 point 4 degree, m angle Z similar to 26 point 6 degree.
Option B
C
Y Z similar to 12 point 9, m angle X similar to 17 point 4 degree, m angle Z similar to 94 point 6 degree.
Option C
D
Y Z similar to 95 point 4, m angle X similar to 26 point 7 degree, m angle Z similar to 85 point 4 degree.
Option D

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