anonymous
  • anonymous
Simplify: 3+2i over 4-i
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Nnesha
  • Nnesha
multiply top and bottom of the fraction by conjugate of the denominator
Nnesha
  • Nnesha
what is the `conjugate` of 4-i ? do you know ?
anonymous
  • anonymous
Welcome to openstudy!

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

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