AnswersMO-Algebra II APerforming Operations with Complex Numbers

Powers and Roots of Complex Numbers Answers

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Two cell phone towers were used to determine the location of an individual calling for assistance. The signal from one tower is represented by r = + sin(θ), and the signal from the other tower by r = 2sin(θ). The points of intersection of the curves are the possible locations of the individual. Which coordinate is one of the possible locations?

Question illustration
A
(Negative StartRoot 3 EndRoot, StartFraction 7 pi Over 6 EndFraction)
Option A
B
(Negative StartRoot 3 EndRoot, StartFraction 5 pi Over 6 EndFraction)
Option B
C
(StartRoot 3 EndRoot, StartFraction 7 pi Over 6 EndFraction)
Option C
D
(StartRoot 3 EndRoot, StartFraction 5 pi Over 6 EndFraction)
Option D
2
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A choir is performing in front of an audience. A microphone is placed in front of the choir to capture sound. Which polar equation represents the microphone the choir is using?

A
r = 4cos(2θ)
B
r = 4cos(4θ)
C
r = 4 + cos(θ)
D
r = 4 + 4cos(θ)
3

Which equation represents the polar form of x – y = 0?

A
θ = 0
B
Theta = StartFraction pi Over 4 EndFraction
Option B
C
Theta = StartFraction 3 pi Over 4 EndFraction
Option C
D
θ = π
4

Which graph represents the polar curve r = 3 – 2cos(θ)?

A
On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, pi). It has an inner loop at (0, 0).
Option A
B
On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, StartFraction 3 pi Over 2 EndFraction). It has an inner loop at (0, 0).
Option B
C
On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (5, pi). It has a convex at (0, 0).
Option C
D
On a polar coordinate plane, a circle crosses the x-axis at (0, 0) and (6, StartFraction 3 pi Over 2 EndFraction). It has an inner loop at (0, 0).
Option D
5

Which graph shape represents the polar curve r = 1 + 4sin(θ)?

A
a cardioid
B
a rose curve
C
a limaçon with an inner loop
D
a limaçon without an inner loop
6

Which graph represents points on the polar curve r = 6cos(θ)?

A
On a polar coordinate plane, points are at (0, 0), (6, 0), (4, StartFraction pi Over 4 EndFraction), and (4, StartFraction 7 pi Over 4 EndFraction).
Option A
B
On a polar coordinate plane, points are at (0, 0), (6, StartFraction pi Over 2 EndFraction), (4.5, StartFraction pi Over 4 EndFraction), and (4.5, StartFraction 3 pi Over 4 EndFraction).
Option B
C
On a polar coordinate plane, points are at (0, 0), (6, pi), (4.5, StartFraction 5 pi Over 4 EndFraction), and (4.5, StartFraction 3 pi Over 4 EndFraction).
Option C
D
On a polar coordinate plane, points are at (0, 0), (6, StartFraction 3 pi Over 2 EndFraction), (4.5, StartFraction 5 pi Over 4 EndFraction), and (4.5, StartFraction 7 pi Over 4 EndFraction).
Option D
7

The equation r = 3cos(6θ) represents a rose curve. How many petals does the graph contain?

A
3
B
6
C
12
D
18
8

The equation r = 4sin(θ) represents a circle. What is the radius of the circle, and what is the symmetry of the graph?

A
The radius is 2 units, and the graph is symmetric about the line .
Option A
B
The radius is 4 units, and the graph is symmetric about the line .
Option B
C
The radius is 2 units, and the graph is symmetric about the polar axis.
D
The radius is 4 units, and the graph is symmetric about the polar axis.
9

Which equation represents the rectangular form of ?

Question illustration
A
StartRoot 3 EndRoot x minus y = 0
Option A
B
StartRoot 3 EndRoot x + y = 0
Option B
C
StartRoot 3 EndRoot x minus 3 y = 0
Option C
D
StartRoot 3 EndRoot x + 3 y = 0
Option D
10

An experiment determines that the polar equation r = 5 + 6cos(θ), where r is in meters, represents the greatest distance between two individuals that still allows them to hear each other speak. Which curve represents this scenario?

A
On a polar coordinate plane, a circle goes through (3.75, StartFraction pi Over 2 EndFraction) and (3.75, StartFraction 3 pi Over 2 EndFraction).
Option A
B
On a polar coordinate plane, a circle goes through (4, StartFraction pi Over 2 EndFraction) and (4, StartFraction 3 pi Over 2 EndFraction).
Option B
C
On a polar coordinate plane, a circle goes through (0, 0) and (11, 0). It has an inner loop at (0, 0).
Option C
D
On a polar coordinate plane, a circle goes through (0, 0) and (12, 0). It has a convex at (0, 0).
Option D

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