AnswersOK-Algebra II APerforming Operations with Complex Numbers

Performing Operations with Complex Numbers Answers

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What is the multiplicative identity of the complex number –4 + 8i?

0
0
1
1
–
–4 + 8i
4
4 – 8i
2
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What is the value of ?

Question illustration
2
2 – 6i
2
2 + 6i
3
3 – 3i
3
3 + 3i
3

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–3 + i) + (18 + 5i)?

(
(–3 + i) + (18 + 5i) + 0
–
–3 + (i + 18) + 5i
(
(–3 + 18) + (i + 5i)
–
–(3 – i) + (18 + 5i)
4

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

1
13 + 3i
1
17 + 3i
2
24 – 147i
2
24 + 147i
5

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

2
20 – 4i
2
20 + 16i
2
28 + 16i
2
28 – 4i
6

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

(
(8 + 6i) = (6i + 8)
(
(8 + 6i)(7 – 9i) = (7 – 9i)(8 + 6i)
(
(8 + 6i)(7 – 9i) = (8 + 6i)(7 – 9i)(1)
(
(8 + 6i) = (8 + 6i + 0)
7

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

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

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?

H
Helene incorrectly used the commutative property by changing the order of the two complex numbers.
H
Helene incorrectly used the associative property by changing the order of the two complex numbers.
H
Helene incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.
H
Helene incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
9

Which equation shows an example of the associative property of addition?

(
(–7 + i) + 7i = –7 + (i + 7i)
(
(–7 + i) + 7i = 7i + (–7i + i)
7
7i × (–7i + i) = (7i – 7i) + (7i × i)
(
(–7i + i) + 0 = (–7i + i)
10

Which equation illustrates the identity property of multiplication?

(
(x + yi) × z = (xz + yzi)
(
(x + yi) × 0 = 0
(
(x + yi) × (z + wi) = (z + wi) × (x + yi)
(
(x + yi) × 1 = (x + yi)

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