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Operations with Complex Numbers Answers

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

A
5
B
9 + 4i
C
9 – 4i
D
13
3

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

A
–8 – 3i
B
–8 + 3i
C
8 – 3i
D
8 + 3i
4

Evaluate when and .

Question illustration
A
29 i
Option A
B
29 i minus 20
Option B
C
Negative 21 i
Option C
D
29
Option D
5

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
7

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)
8

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
9

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
10

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.
11

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

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