AnswersMO-Algebra II APerforming Operations with Complex Numbers

Performing Operations with Complex Numbers Answers

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1
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Which equation illustrates the identity property of multiplication?

A
(x + yi) × z = (xz + yzi)
B
(x + yi) × 0 = 0
C
(x + yi) × (z + wi) = (z + wi) × (x + yi)
D
(x + yi) × 1 = (x + yi)
2
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Which expression is equivalent to ?

Question illustration
A
–5i – 2
B
–4i – 2
C
4i – 2
D
5i – 2
3

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) + 0
B
–3 + (i + 18) + 5i
C
(–3 + 18) + (i + 5i)
D
–(3 – i) + (18 + 5i)
4

Which equation is an example of the commutative property of multiplication?

A
(8 + 6i) = (6i + 8)
B
(8 + 6i)(7 – 9i) = (7 – 9i)(8 + 6i)
C
(8 + 6i)(7 – 9i) = (8 + 6i)(7 – 9i)(1)
D
(8 + 6i) = (8 + 6i + 0)
5

Daine simplified the expression below. 8(1 + 2i) – (7 – 3i) = 1 + 5iWhat mistake did Daine make?

A
He did not apply the distributive property correctly for 8(1 + 2i).
B
He did not distribute the subtraction sign correctly for 7 – 3i.
C
He added the real number and coefficient of i in 8(1 + 2i).
D
He multiplied the two complex numbers when he should have subtracted.
6

What is the sum of 15 – 6i and –2 + 9i?

A
13 + 3i
B
17 + 3i
C
24 – 147i
D
24 + 147i
7

Which property of addition is shown below? If x = 1 + 2i and y = –1 – 2i, then x + y = 0.

A
commutative property
B
identity property
C
associative property
D
inverse property
8

Which property of addition is shown below? 3 + 4i + 5 + 6i = 3 + 5 + 4i + 6i

A
identity property
B
associative property
C
commutative property
D
inverse property
9

Helene is finding the sum (9 + 10i) + (–8 + 11i). She rewrites the sum as (–8 + 11)i + (9 + 10)i. Which statement explains the property of addition that she made an error in using?

A
Helene incorrectly used the commutative property by changing the order of the two complex numbers.
B
Helene incorrectly used the associative property by changing the order of the two complex numbers.
C
Helene incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.
D
Helene incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
10

What is the value of the product (4 – 2i)(6 + 2i)?

A
20 – 4i
B
20 + 16i
C
28 + 16i
D
28 – 4i

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