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

Operations with Complex Numbers Answers

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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
2
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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
3

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.
4

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
5

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)
6

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

What is the value of (–7 + 3i) – (2 – 6i)?

A
–9 + 9i
B
–9 – 3i
C
–5 – 3i
D
–5 + 9i
8

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
9

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
10

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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