AnswersCUSD Advanced Math A 5.0Unit Test

Unit Test — Unit test Answers

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The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 22i. Which statement must be true about the complex numbers?

A
The complex numbers have equal imaginary coefficients.
B
The complex numbers have equal real numbers.
C
The complex numbers have opposite imaginary coefficients.
D
The complex numbers have opposite real numbers.
2
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Which property of multiplication is shown below? If x = 3 + 4i and y = 5 + 6i, x × y = y × x.

A
commutative property
B
identity property
C
distributive property
D
associative property
3

Which values of x and y would make the following expression represent a real number? (6 + 3i)(x + yi)

A
x = 6, y = 0
B
x = –3, y = 0
C
x = 6, y = –3
D
x = 0, y = –3
4

Rectangular coordinates and polar coordinates both represent the same complex number z.Which set of equations demonstrates why both sets of coordinates represent the same number?

Question illustration
A
r = StartRoot 3 EndRoot + StartRoot 3 EndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (1) = StartFraction pi over 4 EndFraction
Option A
B
r = StartRoot 3 EndRoot + StartRoot 3 EndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (StartRoot 3 EndRoot) = StartFraction pi over 4 EndFraction
Option B
C
r = StartStartRoot (StartRoot 3 EndRoot) squared + (StartRoot 3 EndRoot) squared EndEndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (1) = StartFraction pi Over 4 EndFraction
Option C
D
r = StartStartRoot (StartRoot 3 EndRoot) squared + (StartRoot 3 EndRoot) squared EndEndRoot = StartRoot 6 EndRoot and theta = inverse tangent of (StartRoot 3 EndRoot) = StartFraction pi Over 4 EndFraction
Option D
5

A point of the form 25 +bi is 37 units from 13 – 31i. What is the value of b?

A
4
B
6.6
C
36.6
D
40.6
6

Which expression is equivalent to (3 + 5i)2?

A
–16 + 30i
B
6 + 34i
C
–16 – 34i
D
16 + 30i
7

Review the four points on the complex plane.

Question illustration
A
point A
B
point B
C
point C
D
point D
8

Review the graph of complex number z.

Question illustration
A
(cos(135°) + isin(135°))
Option A
B
(cos(135°) + isin(135°))
Option B
C
(cos(225°) + isin(225°))
Option C
D
(cos(225°) + isin(225°))
Option D
9

The following statements are about finding a midpoint of a segment in the complex plane. Which statement is false?

A
The midpoint is the average of the endpoints.
B
First add the endpoints and then multiply by 1/2.
C
First subtract the endpoints and then divide by 2.
D
The midpoint of complex conjugates will lie on the x-axis.
10

An isosceles triangle’s altitude will bisect its base. Which expression could be used to find the area of the isosceles triangle above?

Question illustration
A
StartFraction start root 40 end root . start root 40 end root over 2 EndFraction
Option A
B
StartFraction start root 40 end root . start root 68 end root over 2 EndFraction
Option B
C
StartFraction start root 232 end root . start root 288 end root over 2 EndFraction
Option C
D
StartFraction start root 232 end root . start root 164 end root over 2 EndFraction
Option D
11

What are the conjugate and modulus of –14 – 2i?

A
14 + 2i and
Option A
B
14 + 2i and
Option B
C
–14 + 2i and
Option C
D
–14 + 2i and
Option D
12

The radar system in an airport determines the location of inbound and outbound planes once they are within range. The range, based on the signal from the tower, is represented by the polar equation r = 10cos(θ). Which graph represents the signal range of the airport’s radar system?

A
On a polar coordinate plane, a circle goes through (0, 0) and (10, 0).
Option A
B
On a polar coordinate plane, a circle goes through (0, 0) and (10, StartFraction 3 pi Over 2 EndFraction).
Option B
C
On a polar coordinate plane, a circle goes through (0, 0) and (10, pi).
Option C
D
On a polar coordinate plane, a circle goes through (0, 0) and (10, StartFraction pi Over 2 EndFraction).
Option D
13

Which graph represents points on the polar curve r = –4sin(3θ)?

A
On a polar coordinate plane, points are at (4, StartFraction 2 pi Over 4 EndFraction), (4, 0), and (4, StartFraction 4 pi Over 3 EndFraction).
Option A
B
On a polar coordinate plane, points are at (4, pi), (4, StartFraction pi Over 3 EndFraction), and (4, StartFraction 5 pi Over 3 EndFraction).
Option B
C
On a polar coordinate plane, points are at (4, StartFraction pi Over 6 EndFraction), (4, StartFraction 5 pi Over 6 EndFraction), and (4, StartFraction 3 pi Over 2 EndFraction).
Option C
D
On a polar coordinate plane, point are at (4, StartFraction pi Over 2 EndFraction), (4, StartFraction 11 pi Over 6 EndFraction), (4, StartFraction 7 pi Over 6 EndFraction).
Option D
14

Which equation represents the rectangular form of r = 8?

A
x2 + y2 = 16
B
x2 + y2 = 64
C
StartRoot x squared + y squared EndRoot = 16
Option C
D
StartRoot x squared + y squared EndRoot = 64
Option D

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