How to simplify: (1-3i)(2+i)/(2-i) ?

Question

luigi0210 · Answer

$$\frac{ (1-3i)(2+i) }{ 2-i }$$

luigi0210 · Answer

Is that it?

anonymous · Answer

yes! @Luis_Rivera

luigi0210 · Answer

Well then all you do is FOIL the top

anonymous · Answer

I got 5(I+1)/(2-i) so far

anonymous · Answer

@Luigi0210 would this be one of those situtations when you may mulitply by the reciprical "2+i"..?

luigi0210 · Answer

You could just leave it as $$\frac{ 5-5i }{ 2-i }$$

luigi0210 · Answer

*conjugate, and yes sir!

luigi0210 · Answer

So just as viper says, multiply the top and bottom by the conjugate of 2+i

anonymous · Answer

@Luigi0210 Are you sure you cant simplify it because my teacher did (?... (-2) ) .. He took off points for not simplifying

anonymous · Answer

OH I just saw that okay so 5(I+1)(2+i)

luigi0210 · Answer

$$\frac{ 5-5i }{ 2-i }*\frac{ 2+i }{ 2+i }=\frac{ 10+5i-10i-5i^2 }{ 4-i^2 }$$
Can you finish it from here Miss Princess?

anonymous · Answer

(1 - 3i) x 2 + i / 2 - i = 3 - 1

anonymous · Answer

@Luigi0210 Oh sorry I forgot! Yea ..

anonymous · Answer

then youd combine like terms

anonymous · Answer

would you expand the denom.

luigi0210 · Answer

$$i^2=-1$$

anonymous · Answer

Did you get -5i+15/5 ??

luigi0210 · Answer

Yup, and simplified down farther it is 3-i.

luigi0210 · Answer

*or -i+3

anonymous · Answer

Haha yea it's 3 - i

anonymous · Answer

The works up there sorry I don't want to post it again haha!

luigi0210 · Answer

What up pooper? :D

anonymous · Answer

Nothing I'm just bored so I decided to help people with math :/ haha
Marios bro

luigi0210 · Answer

Ah, interesting 
I know :P

anonymous · Answer

Haha!

anonymous · Answer

I'm going to continue on now! :D

luigi0210 · Answer

ha, well alright.. good day to you :P

anonymous · Answer

thnx!

anonymous · Answer

You too luigi! :*

luigi0210 · Answer

No problem :P Enjoy the rest of your day you two :P