Question

Simplify:
3+2i over 4-i

Answer 1

multiply top and bottom of the fraction by conjugate of the denominator

Answer 2

what is the `conjugate` of 4-i ? do you know ?

Answer 3

Welcome to openstudy!

Answer 4

thanks :=)

Answer 5

lol

Answer 6

I don't know the conjugate ;~;

Answer 7

here is an example the conjugate of a+bi is `a-bi` so change the sign of the imaginary term

Answer 8

I don't get how to do that either...

Answer 9

conjugate of a+bi is `a-bi` right
so what's the difference btw `a+bi` and `a-bi` ?

Answer 10

The + and -

Answer 11

yes right so you should change the sign of imaginary number
`i` = imaginary

Answer 12

so what's the conjugate of 4-i ?

Answer 13

4+i?

Answer 14

yes right!
now multiply \[\huge\rm \frac{ 3+2i }{ 4-i} \times \frac{ 4+i }{ 4+i }\]

Answer 15

12+3i over 16?

Answer 16

show ur steps please how did you get that ?

Answer 17

I don't know how I did that.
I have no idea how i did that.

Answer 18

then why did you post that ?

Answer 19

I was hoping it was right..

Answer 20

familiar with the foil method ?

Answer 21

Yeah.

Answer 22

i know that's one of ur option.

Answer 23

alright good apply foil method \[\huge\rm \frac{ (3+2i)(4+i) }{ (4-i)(4+i) }\]
(3+2i)(4+i) = ??

Answer 24

I think it's 12+14i? That's what I got..

Answer 25

okay plz show ur work so i can look over to find out mistakes :=)

Answer 26

that would be great!

Answer 27

(3+2i)(4+i)
12+3i+8i+3i
12+6i+8i
12+14i

Answer 28

nice thanks
so 2i times i = ??

Answer 29

Not 3i?

Answer 30

OH
OH
-2

Answer 31

yes right
i times i= i^2
and i^2 =-1
so 2(-1) = -1 now fix it

Answer 32

so it's \[12+3i+8i-2\]

Answer 33

So I was mostly right.
Now what.

Answer 34

now combine like terms
12+3i+8i-2 = ?

Answer 35

10+11i

Answer 36

looks right!
now simplify the denominator (4-i)(4+i)= ?

Answer 37

17!

Answer 38

right that's denominator so what would be the final answer ?

Answer 39

\[\frac{ 10+11i}{ 17}\]

Answer 40

looks good ! great job !

Answer 41

Thank you~

Answer 42

np :=)