Question:

Find real values for k for which (z - ki) is a factor of the polynomial equation: $\displaystyle z^4-2z^3+7z^2-4z+10=0$

What I did:

I tried splitting them up into two different quadratic equations to use the Qudaratic formula to find the complex roots. But I ended up with a mess of unknowns and it just seemed to complicated and messy to be the right direction.

Any hints as to how I should tackle these questions?