Question

Given that x = -2 - 3i and y = 4 + 2i , Match The Expressions.

Answer 1

3y - 2x --> 16 + 12i

-3x · y --> 6 + 48i

x · 2y --> -4 - 32i

x - y --> -6 - 5i

Explanation:

Work each one out.

3y - 2x

3(4 + 2i) - 2(-2 - 3i)

12 + 6i + 4 + 6i

16 + 12i

-3x · y

-3(-2 - 3i) · (4 + 2i)

(6 +9i) · (4 + 2i)

24 + 12i + 26i - 18

6 +48i

x · 2y

(-2 - 3i) · 2(4 + 2i)

(-2 - 3i) · (8 + 4i)

-16 - 8i - 24i +12

-4 - 32i

x - y

(-2 - 3i) - (4 + 2i)

-6 - 5i

Answer 2

`3y-2x=16+12i`

`-3x \cdot y=6+48i`

`x \cdot 2y=-4-32i`

`x-y=-6-5i`

Explanation:

Given:

`x=-2-3i`

`y=4+2i`

---

1st problem:

`3y-2x`

`3(4+2i)-2(-2-3i)`

Distribute:

`12+6i+4+6i`

Combine like terms:

`16+12i`

---

2nd problem:

`-3x \cdot y`

`-3(-2-3i) cdot (4+2i)`

`-3(-2-3i)(4+2i)`

Distribute -3 to first factor:

`(6+9i)(4+2i)`

Use foil to simplify:

`24+12i+36i+18i^2`

Replace
`i^2` with -1:

`24+48i-18`

Combine like terms:

`6+48i`

---

3rd problem:

`x \cdot 2y`

`(-2-3i) \cdot 2(4+2i)`

Distribute 2 to the second factor:

`(-2-3i) \cdot (8+4i)`

`(-2-3i)(8+4i)`

Use foil to simplify:

`-16-8i-24i-12i^2`

Replace
`i^2` with -1:

`-16-32i+12`

Combine like terms:

`-4-32i`

----

4th problem:

`(-2-3i)-(4+2i)`

Distribute:

`-2-3i-4-2i`

Combine like terms:

`-2-4-3i-2i`

Simplify:

`-6-5i`