Vectors and Their Components Answers
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21
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What is the rectangular form of 17(cos(315°) + isin(315°))?
A
StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction minus StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction i
B
StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction + StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction i
C
Negative StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction minus StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction i
D
Negative StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction + StartFraction 17 StartRoot 2 EndRoot Over 2 EndFraction i
22
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Which graph represents the polar curve r = 4cos(3θ)?
A
On a polar coordinate plane, a rose curve has 8 petals. Four petals are on the x and y-axes.
B
On a polar coordinate plane, a rose curve has 3 petals. One petal goes to (4, 0), another to (4, StartFraction 2 pi Over 3), and another goes to (4, StartFraction 4 pi Over 3 EndFraction).
C
On a polar coordinate plane, a rose curve has 8 petals. The petals are not on the x- or y-axes.
D
On a polar coordinate plane, a rose curve has 3 petals. One petal goes to (4, StartFraction pi Over 6 EndFraction), another to (4, StartFraction 5 pi Over 6), and another goes to (4, StartFraction 3 pi Over 2 EndFraction).
23
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 .
B
The radius is 4 units, and the graph is symmetric about the line .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.24
What is the polar form of ?
A
18(cos(120°) + isin(120°))B
18(cos(150°) + isin(150°))C
324(cos(120°) + isin(120°))D
324(cos(150°) + isin(150°))25
If z = 13 – 7i, what is the value of |z|?
A
6B
2C
StartRoot 218 EndRootD
2026
The equation r = 3cos(6θ) represents a rose curve. How many petals does the graph contain?
A
3B
6C
12D
1827
The equation r = 3cos(6θ) represents a rose curve. How many petals does the graph contain?
A
3B
6C
12D
1828
Which equation shows an example of the associative property of addition?
A
(–7 + i) + 7i = –7 + (i + 7i)B
(–7 + i) + 7i = 7i + (–7i + i)C
7i × (–7i + i) = (7i – 7i) + (7i × i)D
(–7i + i) + 0 = (–7i + i)29
Which graph represents the polar curve r = 4cos(3θ)?
A
On a polar coordinate plane, a rose curve has 8 petals. Four petals are on the x and y-axes.B
On a polar coordinate plane, a rose curve has 3 petals. One petal goes to (4, 0), another to (4, StartFraction 2 pi Over 3), and another goes to (4, StartFraction 4 pi Over 3 EndFraction).C
On a polar coordinate plane, a rose curve has 8 petals. The petals are not on the x- or y-axes.D
On a polar coordinate plane, a rose curve has 3 petals. One petal goes to (4, StartFraction pi Over 6 EndFraction), another to (4, StartFraction 5 pi Over 6), and another goes to (4, StartFraction 3 pi Over 2 EndFraction).30
Which graph represents –4 + 3i?
A
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is at (negative 4, 3).B
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is at (negative 3, 4).C
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is at (3, negative 4).D
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is at (4, negative 3).31
Review the four points shown on the polar coordinate system.
A
point AB
point BC
point CD
point D32
Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–3 + i) + (18 + 5i)?
A
(–3 + i) + (18 + 5i) + 0B
–3 + (i + 18) + 5iC
(–3 + 18) + (i + 5i)D
–(3 – i) + (18 + 5i)33
Which expression is equivalent to ?
A
6 (cosine ( StartFraction pi over 2 EndFraction) plus i sine (StartFraction pi over 2 EndFraction))
B
6 (cosine ( StartFraction pi over 6 EndFraction) plus i sine (StartFraction pi over 6 EndFraction))
C
8 (cosine ( StartFraction pi over 2 EndFraction) plus i sine (StartFraction pi over 2 EndFraction))
D
8 (cosine ( StartFraction pi over 6 EndFraction) plus i sine (StartFraction pi over 6 EndFraction))
34
Which equation represents the polar form of x – y = 0?
A
θ = 0B
Theta = StartFraction pi Over 4 EndFraction
C
Theta = StartFraction 3 pi Over 4 EndFraction
D
θ = π35
What is the rectangular form of z = ?
A
z = 20 minus 20 I StartRoot 3 EndRoot
B
z = 20 StartRoot 3 EndRoot minus 20 i
C
z = negative 20 StartRoot 3 EndRoot minus 20 i
D
z = negative 20 minus 20 I StartRoot 3 EndRoot
36
What is the distance on the unit circle between successive fourth roots of ?
A
StartFraction pi Over 3 EndFraction
B
StartFraction pi Over 2 EndFraction
C
StartFraction 2 pi Over 3 EndFraction
D
Pi
37
What is (1 +i)5?
A
–4 – 4iB
–4 + 4iC
4 – 4iD
4 + 4i38
Which graph represents ?
A
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (0.5, 1).
B
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (1, 1.75).
C
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (negative 0.5, 1).
D
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (negative 1, 1.75).
39
Which equation illustrates the identity property of multiplication?
A
(x + yi) × z = (xz + yzi)B
(x + yi) × 0 = 0C
(x + yi) × (z + wi) = (z + wi) × (x + yi)D
(x + yi) × 1 = (x + yi)40
What is the polar form of ?
A
2 StartRoot 6 EndRoot (cosine (StartFraction 2 pi Over 3 EndFraction) + I sine (StartFraction 2 pi Over 3 EndFraction) )B
4 StartRoot 3 EndRoot (cosine (StartFraction 2 pi Over 3 EndFraction) + I sine (StartFraction 2 pi Over 3 EndFraction) )C
2 StartRoot 6 EndRoot (cosine (StartFraction 4 pi Over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )D
4 StartRoot 3 EndRoot (cosine (StartFraction 4 pi Over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )Did you find these answers helpful?
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