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Klio2033 [76]
3 years ago
15

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

Mathematics
2 answers:
shtirl [24]3 years ago
6 0

Answer:

3y-2x=16+12i

-3x \cdot y=6+48i

x \cdot 2y=-4-32i

x-y=-6-5i

Step-by-step 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

svp [43]3 years ago
5 0

Answer:

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

-3x · y --> 6 + 48i

x · 2y --> -4 - 32i

x - y --> -6 - 5i

Step-by-step explanation:

Work each one out.

<u>3y - 2x</u>

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

12 + 6i + 4 + 6i

16 + 12i

<u>-3x · y</u>

-3(-2 - 3i) · (4 + 2i)

(6 +9i) · (4 + 2i)

24 + 12i + 26i - 18

6 +48i

<u>x · 2y</u>

(-2 - 3i) · 2(4 + 2i)

(-2 - 3i) · (8 + 4i)

-16 - 8i - 24i +12

-4 - 32i

<u>x - y</u>

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

-6 - 5i

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