Question

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

Answer 1

Answer:

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

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

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

$x-y=-6-5i$

Step-by-step explanation:

Given:

$x=-2-3i$

$y=4+2i$

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1st problem:

$3y-2x$

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

Distribute:

$12+6i+4+6i$

Combine like terms:

$16+12i$

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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:

$6+48i$

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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:

$-4-32i$

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4th problem:

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

Distribute:

$-2-3i-4-2i$

Combine like terms:

$-2-4-3i-2i$

Simplify:

$-6-5i$

Answer 2

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.

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