..Show that z^4 - 2z3 + 6z^2 -8z + 8 =0 has a root of the form ki, where k is real. Hence solve the equation z^4 - 2z3 + 6z^2 -8z + 8 =0

my steps are

let f(x) = z^4 - 2z3 + 6z^2 -8z + 8

since, ki is a root

f(ki)= z^4 - 2z3 + 6z^2 -8z + 8 = 0

substituting ki inside,

i get (k^2 -2)(k^2 -4) +2k(k^2 -4)i =0 Notice that this factorises as .

im not sure how to proceed at this point..

the answer is z=2i, -2i, 1+i or 1-i