AnswersFall 24 GMS Advanced Algebra Concepts and Connections AOperations with Complex Numbers

Operations with Complex Numbers Answers

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1
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Melissa and Tomas are playing a game with complex numbers. If Melissa has a score of 5 – 4i and Tomas has a score of 3 + 2i, what is their total score?

A
8 – 6i
B
8 + 6i
C
8 – 2i
D
8 + 2i
2
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What is the value of (–7 + 3i) – (2 – 6i)?

A
–9 + 9i
B
–9 – 3i
C
–5 – 3i
D
–5 + 9i
3

Which property of multiplication is shown below? If x = a + bi and y = c + di, x × y = y × x.

A
commutative property
B
identity property
C
distributive property
D
associative property
4

Which property of addition is shown in the equation below?a + bi + 0 + 0i = a + bi

A
commutative property
B
inverse property
C
identity property
D
associative property
5

Aiko is finding the sum (4 + 5i) + (–3 + 7i). She rewrites the sum as (–3 + 7)i + (4 + 5)i. Which statement explains the error Aiko made by using a mathematical property incorrectly?

A
Aiko incorrectly used the commutative property by changing the order of the two complex numbers.
B
Aiko incorrectly used the associative property by changing the order of the two complex numbers.
C
Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.
D
Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
6

What is the additive inverse of the complex number –8 + 3i?

A
–8 – 3i
B
–8 + 3i
C
8 – 3i
D
8 + 3i
7

Donte simplified the expression below.What mistake did Donte make?

Question illustration
A
He did not apply the distributive property correctly for 4(1 + 3i).
B
He did not distribute the subtraction sign correctly for 8 – 5i.
C
He added the real number and coefficient of i in 4(1 + 3i).
D
He added the two complex numbers instead of subtracted.
8

Which equation illustrates the identity property of multiplication?

A
(a + bi) × c = (ac + bci)
B
(a + bi) × 0 = 0
C
(a + bi) × (c + di) = (c + di) × (a + bi)
D
(a + bi) × 1 = (a + bi)
9

Which equation demonstrates the additive identity property?

A
(7 + 4 i) + (7 minus 4 i) = 14
Option A
B
(7 + 4 i) + 0 = 7 + 4 i
Option B
C
(7 + 4 i) (1) = 7 + 4 i
Option C
D
(7 + 4 i) + (negative 7 minus 4 i) = 0
Option D
10

Which property of addition is shown below?a + bi + c + di = a + c + bi + di

A
identity property
B
associative property
C
commutative property
D
inverse property
11

What is the value of the product (3 – 2i)(3 + 2i)?

A
5
B
9 + 4i
C
9 – 4i
D
13
12

The relationship between voltage, E, current, I, and resistance, Z, is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 – i, what is the voltage of the circuit?

A
4 – i
B
4 + i
C
8 + i
D
8 + 7i
13

What is the additive inverse of the complex number 9 – 4i?

A
–9 – 4i
B
–9 + 4i
C
9 – 4i
D
9 + 4i
14

Melissa and Tomas are playing a game with complex numbers. If Melissa has a score of 5 – 4i and Tomas has a score of 3 + 2i, what is their total score?

A
8 – 6i
B
8 + 6i
C
8 – 2i
D
8 + 2i
15

Which equation illustrates the identity property of multiplication?

A
(a + bi) × c = (ac + bci)
B
(a + bi) × 0 = 0
C
(a + bi) × (c + di) = (c + di) × (a + bi)
D
(a + bi) × 1 = (a + bi)
16

What is the additive inverse of the complex number –8 + 3i?

A
–8 – 3i
B
–8 + 3i
C
8 – 3i
D
8 + 3i
17

Aiko is finding the sum (4 + 5i) + (–3 + 7i). She rewrites the sum as (–3 + 7)i + (4 + 5)i. Which statement explains the error Aiko made by using a mathematical property incorrectly?

A
Aiko incorrectly used the commutative property by changing the order of the two complex numbers.
B
Aiko incorrectly used the associative property by changing the order of the two complex numbers.
C
Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.
D
Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
18

Which property of addition is shown below?If x = a + bi and y = –a – bi, x + y = 0.

A
commutative property
B
identity property
C
associative property
D
inverse property
19

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

A
(–4 + i) + 4i = –4 + (i + 4i)
B
(–4 + i) + 4i = 4i + (–4i + i)
C
4i × (–4i + i) = (4i – 4i) + (4i × i)
D
(–4i + i) + 0 = (–4i + i)
20

Which property of addition is shown below?a + bi + c + di = a + c + bi + di

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

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