complex quadratic polynomial

QUESTION: Find a (complex) quadratic polynomial P(z)=a+bz+cz2 which interpolates the data: (-1,i),(0,i), (6 i, 0)

Write your answers a ,b, c in form x + iy

My Work:

So I have three different equations, using my x coordinate for my z values and my y coordinate as my P(z) values.

Equations:

i = a - b + c

i = a

0 = a + 6ib

I (tried) to solve each value by matrix reduction

__1_-1__1__i

__1_0__0 __i

__1_6i_-36_0

__1__-1___ 1____i

__0__ 1__(-6/i) _(-i/6)

__0__-1____1___0

(i continue to solve it until i get...):

a=i

b+(6i)c = -1/6

(1+6i)c = -1/6

if this IS right, i don't know how to actually solve the system

i end up getting b=c,

but if they answer has to be in x+iy how do i put it in this form??

thanks for the help!