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
So I have three different equations, using my x coordinate for my z values and my y coordinate as my P(z) values.
i = a - b + c
i = a
0 = a + 6ib
I (tried) to solve each value by matrix reduction
__0__ 1__(-6/i) _(-i/6)
(i continue to solve it until i get...):
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!