AnswersMO-Algebra II A-CRPerforming Operations with Complex Numbers

Graphing Polar Equations Answers

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1
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What is the argument of z = ?

Question illustration
A
Negative StartFraction pi Over 3 EndFraction
Option A
B
Negative StartFraction pi Over 6 EndFraction
Option B
C
StartFraction pi Over 6 EndFraction
Option C
D
StartFraction pi Over 3 EndFraction
Option D
2
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For the complex number z = 12 + i, what is ?

Question illustration
A
12 – i
B
12 + i
C
–12 – i
D
–12 + i
3

What is the polar form of ?

Question illustration
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) )
4

What is the rectangular form of z = ?

Question illustration
A
z = 20 minus 20 I StartRoot 3 EndRoot
Option A
B
z = 20 StartRoot 3 EndRoot minus 20 i
Option B
C
z = negative 20 StartRoot 3 EndRoot minus 20 i
Option C
D
z = negative 20 minus 20 I StartRoot 3 EndRoot
Option D
5

Review the graph of complex number z.

Question illustration
A
5 (cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) )
Option A
B
5 StartRoot 2 EndRoot (cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) )
Option B
C
5 (cosine (negative StartFraction pi Over 4 EndFraction) + I sine (negative StartFraction pi Over 4 EndFraction) )
Option C
D
5 StartRoot 2 EndRoot (cosine (negative StartFraction pi Over 4 EndFraction) + I sine (negative StartFraction pi Over 4 EndFraction) )
Option D
6

Review the graph of complex number z.

Question illustration
A
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (2, 5).
B
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (5, negative 2).
C
On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (2, negative 5).
D
Option
7

Which graph represents ?

Question illustration
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).
Option A
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).
Option B
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).
Option C
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).
Option D
8

What is the polar form of ?

Question illustration
A
18(cos(120°) + isin(120°))
B
18(cos(150°) + isin(150°))
C
324(cos(120°) + isin(120°))
D
324(cos(150°) + isin(150°))
9

What is the rectangular form of 12(cos() + isin())?

Question illustration
A
12
B
-12
C
12 + i
D
–12 + i
10

Which pair of equations can be used to verify the rectangular form, z = a + bi, and the polar form of a complex number are equivalent?

A
a = sin(θ) and b = cos(θ)
B
a = cos(θ) and b = sin(θ)
C
a = rsin(θ) and b = rcos(θ)
D
a = rcos(θ) and b = rsin(θ)
11

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).
12

Review the graph of complex number z.

Question illustration
A
2
B
2
C
3
D
StartRoot 10 EndRoot
13

Convert the polar coordinates (5, 6.1) to rectangular coordinates.

A
(0.98, –0.18)
B
(0.98, 0.18)
C
(4.92, –0.91)
D
(4.92, 0.91)
14

Review the four points shown on the polar coordinate system.

Question illustration
A
point A
B
point B
C
point C
D
point D
15

Convert (4, –2) into approximate polar coordinates.

A
r = 3.46; θ = –0.46
B
r = 3.46; θ = 0.46
C
r = 4.47; θ = –0.46
D
r = 4.47; θ = 0.46
16

Review the four points shown on the polar coordinate system.

Question illustration
A
point A
B
point B
C
point C
D
point D

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