Operations with Complex Numbers Answers

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Let x = a + bi and y = c + di and z = f + giWhich statements are true? Check all of the boxes that apply.

A
x + y = y + x
B
(x × y) × z = x × (y × z)
C
x – y = y – x
D
(x + y) + z = x + (y + z)
E
(x – y) – z = x – (y – z)
5

Which addition expression has the sum 8 – 3i ?

A
(9 + 2i) + (1 – i)
B
(9 + 4i) + (–1 – 7i)
C
(7 + 2i) + (1 – i)
D
(7 + 4i) + (–1 – 7i)
6

Is the work shown below correct? Explain your answer.(11 + 2i ) – (3 – 10i ) = 11 + 2i – 3 – 10i = (11 – 3) + (2i – 10i) = 8 – 8i

Answer:

No, the work is incorrect. When subtracting $(3 10i)$, the subtraction sign must be distributed to both terms in the parentheses. This means $(10i)$ should become $10i$. The correct steps should be: $11 2i 3 10i (11 3) (2i 10i) 8 12i$.

7

Which subtraction expression has the difference 1 + 4i?

A
(–2 + 6i) – (1 – 2i)
B
(–2 + 6i) – (–1 – 2i)
C
(3 + 5i) – (2 – i)
D
(3 + 5i) – (2 + i)
10

Question text not available

Answers:
Blank 1:45
Blank 2:41
Blank 3:73
12

Simplify each expression. Select the correct answer from the drop-down menu.

Answers:
−6(3i)(−2i) = 2(3 − i)(−2 + 4i) =:–36
−6(3i)(−2i) = 2(3 − i)(−2 + 4i) =:–4 + 28i
13

–3636–6 – 6i 36i

A
–36
B
36
C
–6 – 6i
D
36i
14

Which pair of complex factors results in a real-number product?

A
15(–15i)
B
3i(1-3i)
C
(8 + 20i)(–8 – 20i)
D
(4+7i)(4-7i)
15

Find the sum of (–4 + i) and (10 – 5i).

A
–3 + 5i
B
–3 - 5i
C
6 – 4i
D
6 – 6i
16

Subtract (3 + 2i) from (–9 – 8i).

A
–17 – 5i
B
–6 – 6i
C
–12 – 10i
D
12 + 10i
20

–2 + 14i –4 + 28i –20 + 20i

A
–2 + 14i
B
–4 + 28i
C
–20 + 20i

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