AnswersMO-Algebra II A-CRPerforming Operations with Complex Numbers

Performing Operations with Complex Numbers — Unit test Answers

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Which equation represents a graph with a vertex at (1, –6)?

A
y = 3x2 + 6x – 3
B
y = 3x2 – 6x – 3
C
y = 3x2 – 8x – 1
D
y = 3x2 – 3x – 6
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 could be the function graphed below?

Question illustration
A
f (x) = StartRoot x minus 5 EndRoot + 1
Option A
B
f (x) = StartRoot x minus 2 EndRoot
Option B
C
f (x) = StartRoot x EndRoot
Option C
D
f (x ) = StartRoot x + 4 EndRoot
Option D
4

Solve for in the equation .

Question illustration
A
x = 3 plus-or-minus StartRoot 23 EndRoot
Option A
B
x = 3 plus-or-minus StartRoot 51 EndRoot
Option B
C
x = 3 plus-or-minus StartRoot 41 EndRoot
Option C
D
x = 3 plus-or-minus StartRoot 5 EndRoot
Option D
5

For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?

A
m greater-than negative StartFraction 25 Over 8 EndFraction
Option A
B
m less-than negative StartFraction 25 Over 8 EndFraction
Option B
C
m less-than StartFraction 25 Over 8 EndFraction
Option C
D
m greater-than StartFraction 25 Over 8 EndFraction
Option D
6

Which equation is the inverse of y = x2 – 36?

A
y = plus-or-minus StartRoot x EndRoot + 6
Option A
B
y = plus-or-minus StartRoot x + 36 EndRoot
Option B
C
y = plus-or-minus StartRoot x EndRoot + 36
Option C
D
y = plus-or-minus StartRoot x squared + 36 EndRoot
Option D
7

Use the zero product property to find the solutions to the equation 2x2 + x – 1 = 2.

A
x = or x = 2
Option A
B
x = –2 or x =
Option B
C
x = or x = 1
Option C
D
x = 1 or x =
Option D
8

What is the greatest possible integer value of x for which is an imaginary number?

Question illustration
A
3
B
4
C
5
D
6
9

Use the zero product property to find the solutions to the equation x2 – 9 = 16.

A
x = –3 or x = 3
B
x = –6 or x = –3
C
x = –5 or x = 5
D
x = 7 or x = 1
10

Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.

A
x = –3 or x = –2
B
x = –3 or x = 2
C
x = –2 or x = 3
D
x = 2 or x = 3
11

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

A
y = negative 6 (x minus 1) squared + 8
Option A
B
y = negative 6 (x + one-fourth) squared + thirteen-eighths
Option B
C
y = negative 6 (x minus one-fourth) squared + nineteen-eighths
Option C
D
y = negative 6 (x minus one-half) squared + seven-halves
Option D
12

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

A
–16 + 30i
B
6 + 34i
C
–16 – 34i
D
16 + 30i
13

Solve for in the equation .

Question illustration
A
x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction
Option A
B
x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction
Option B
C
x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option C
D
x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option D
14

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

A
y = 3 (x minus seven-halves) squared minus StartFraction 27 Over 4 EndFraction
Option A
B
y = 2 (x minus 1) squared minus 11
Option B
C
y = 2 (x minus one-half) squared minus StartFraction 53 Over 4 EndFraction
Option C
D
y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction
Option D
15

For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?

A
0
B
9
C
12
D
16
16

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.
17

Which point shows the location of 5 – 2i on the complex plane below?

Question illustration
A
point A
B
point B
C
point C
D
point D
18

When graphed, which parabola opens downward?

A
y = –3x2
B
y = (x – 3)2
C
y = one-third x squared
Option C
D
y = x2 – 3
19

What is the value of i 97 – i?

A
–i
B
0
C
–2i
D
i Superscript 96
Option D
20

Adam is using the equation (x)(x + 2) = 255 to find two consecutive odd integers with a product of 255. When Adam solves the problem using the zero product property, what do those solutions represent?

A
two possible “first” integers
B
two possible “second” integers
C
the two consecutive odd integers with a product of 255
D
a possible “first” integer and a possible “second” integer

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