Simplify: 3+2i over 4-i

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Simplify: 3+2i over 4-i

Algebra
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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multiply top and bottom of the fraction by conjugate of the denominator
what is the `conjugate` of 4-i ? do you know ?
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Other answers:

thanks :=)
lol
I don't know the conjugate ;~;
here is an example the conjugate of a+bi is `a-bi` so change the sign of the imaginary term
I don't get how to do that either...
conjugate of a+bi is `a-bi` right so what's the difference btw `a+bi` and `a-bi` ?
The + and -
yes right so you should change the sign of imaginary number `i` = imaginary
so what's the conjugate of 4-i ?
4+i?
yes right! now multiply \[\huge\rm \frac{ 3+2i }{ 4-i} \times \frac{ 4+i }{ 4+i }\]
12+3i over 16?
show ur steps please how did you get that ?
I don't know how I did that. I have no idea how i did that.
then why did you post that ?
I was hoping it was right..
familiar with the foil method ?
Yeah.
i know that's one of ur option.
alright good apply foil method \[\huge\rm \frac{ (3+2i)(4+i) }{ (4-i)(4+i) }\] (3+2i)(4+i) = ??
I think it's 12+14i? That's what I got..
okay plz show ur work so i can look over to find out mistakes :=)
that would be great!
(3+2i)(4+i) 12+3i+8i+3i 12+6i+8i 12+14i
nice thanks so 2i times i = ??
Not 3i?
OH OH -2
yes right i times i= i^2 and i^2 =-1 so 2(-1) = -1 now fix it
so it's \[12+3i+8i-2\]
So I was mostly right. Now what.
now combine like terms 12+3i+8i-2 = ?
10+11i
looks right! now simplify the denominator (4-i)(4+i)= ?
17!
right that's denominator so what would be the final answer ?
\[\frac{ 10+11i}{ 17}\]
looks good ! great job !
Thank you~
np :=)

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