Answer:
[tex]3y-2x=16+12i[/tex]
[tex]-3x \cdot y=6+48i[/tex]
[tex]x \cdot 2y=-4-32i[/tex]
[tex]x-y=-6-5i[/tex]
Step-by-step explanation:
Given:
[tex]x=-2-3i[/tex]
[tex]y=4+2i[/tex]
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1st problem:
[tex]3y-2x[/tex]
[tex]3(4+2i)-2(-2-3i)[/tex]
Distribute:
[tex]12+6i+4+6i[/tex]
Combine like terms:
[tex]16+12i[/tex]
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2nd problem:
[tex]-3x \cdot y[/tex]
[tex]-3(-2-3i) cdot (4+2i)[/tex]
[tex]-3(-2-3i)(4+2i)[/tex]
Distribute -3 to first factor:
[tex](6+9i)(4+2i)[/tex]
Use foil to simplify:
[tex]24+12i+36i+18i^2[/tex]
Replace [tex]i^2[/tex] with -1:
[tex]24+48i-18[/tex]
Combine like terms:
[tex]6+48i[/tex]
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3rd problem:
[tex]x \cdot 2y[/tex]
[tex](-2-3i) \cdot 2(4+2i)[/tex]
Distribute 2 to the second factor:
[tex](-2-3i) \cdot (8+4i)[/tex]
[tex](-2-3i)(8+4i)[/tex]
Use foil to simplify:
[tex]-16-8i-24i-12i^2[/tex]
Replace [tex]i^2[/tex] with -1:
[tex]-16-32i+12[/tex]
Combine like terms:
[tex]-4-32i[/tex]
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4th problem:
[tex](-2-3i)-(4+2i)[/tex]
Distribute:
[tex]-2-3i-4-2i[/tex]
Combine like terms:
[tex]-2-4-3i-2i[/tex]
Simplify:
[tex]-6-5i[/tex]
