AnswersMO-Algebra II A-CRPerforming Operations with Complex Numbers

Performing Operations with Complex Numbers Answers

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Let x = a + bi and y = c + di and z = f + gi.Which 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)
3

–2 + 14i ✔ –4 + 28i –20 + 20i

A
–2 + 14i
B
–4 + 28i
C
–20 + 20i
4

–2i 2i–10 + 8i✔ 10 + 8i

A
–2i
B
2i
C
–10 + 8i
D
10 + 8i
5

Question text not available

Answers:
Blank 1:-1
Blank 2:2
8

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)
9

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

36-3636i-36i

A
36
B
-36
C
36i
D
-36i
12

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)
13

–3 + i–3 – i7 + i✔ 7 – i

A
–3 + i
B
–3 – i
C
7 + i
D
7 – i
14

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

Answer:

The work shown is not correct. When distributing the negative sign to the expression (3 10i), the sign of every term inside the parentheses must change. The 10i should have become 10i. Therefore, the expression should have been 11 2i 3 10i, which simplifies to (11 3) (2i 10i) 8 12i.

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
18

✔ –3636–6 – 6i 36i

A
–36
B
36
C
–6 – 6i
D
36i

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