Stuck on Algebra II/Calculus problem

I know I'm surrounded by a bunch of my fellow nerds here on CPF. Perhaps you can lend me some of your brains? I've been trying to crack this synthetic division problem for days. I tried every possible combination but still can't get the answer. Also tried googling it but found nothing useful. Here's the problem:

z^3 + 3z^2 - 2z + 3
-------------------- (the --- line means division)
z-i

...and the quotient is this, with remainder -3i/z-i:

z^2 + (3 + i)z + (-3 + 3i) + -3i/z-i

When attempting to divide this is what I got:

-i . 1 . . 3 . . -2 . . .3
. . . . . .-i . -1-3i .-3+3i
__________________
. . .1 . .3-i . -3-3i . .3i

Please ignore the dots as CPF doesn't allow excess spacing.

Which doesn't match the solution and the signs are the only thing different. No matter what I try I can't switch the signs without affecting something else. Tried factoring out a negative but that doesn't work. I either missed something or there's a rule I'm not aware of. Any help would be great!

Dang, sorry dude, I did that stuff a long time ago but it's Greek to me now. Hopefully somebody here has worked it more recently and still remembers how!

If all else fails, go to the teacher during his/her office hours

Perhaps help can be found here:

http://www.khanacademy.org/math/tri...ional/synthetic-division/v/synthetic-division

If not, I can be of no further assistance.

~ Chance

Man do I NOT miss university lol. Lucky I did this stuff though because its helped me soooo many times. (Sarcasm intended).

Probably could have helped you 10years ago...but not anymore sorry.

Good luck!

Sent from my Galaxy Nexus using Tapatalk

Have you tried plugging in into Wolfram alpha? Thats always my solution when I get stuck haha

Also are you sure you are deciding by (z-i) instead of (z-1)?