Prove that 1+i is a root of the equation z^4+3z^2-6z+10=0. Find all the other roots.
(Check.)
Now, if 1+i is a root, so is 1-i. Thus we know that
is a factor of . So do the division. This gives you a quadratic in z to solve, which you can do by factoring or the quadratic formula or whatnot.