Suppose q(z) = z^3 − z^2 + rz + s, is a complex polynomial with 1 + i and i as zeros. Find r and s and the third complex zero.
The Attempt at a Solution
(z-(1+i)(z-i) = Z^2-z-1-2iz+i
(Z^2-z-1-2iz+i)(z+d) = Z^3+z^2(d-1-zi)-z(d+1+2di-i)-d(1-i)
This is what I have done but I am when I expand the complex zeros I do not get anything close to q(z)