AnswersMO-Algebra II APerforming Operations with Complex Numbers

Performing Operations with Complex Numbers Answers

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

A
13 + 3i
B
17 + 3i
C
24 – 147i
D
24 + 147i
2
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What is the value of ?

Question illustration
A
2 – 6i
B
2 + 6i
C
3 – 3i
D
3 + 3i
3

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)
4

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
5

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)
7

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.
8

Which property of addition is shown in the equation below? c + di + 0 + 0i = c + di

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

Which expression is equivalent to ?

Question illustration
A
–5i – 2
B
–4i – 2
C
4i – 2
D
5i – 2
10

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)

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