Show that the equation \[z ^{3}+(-3+i)z^{2}+(6-3i)z+(-6-8i)=0\] has a pure imaginary root and then solve the equation.
I know how to solve it by setting z=bi but what if the description would have said "has a pure real root " should i use z=a instead?

Haha yeah that troubled me a bit since I always deal with pure imaginary ones :p I assume it's the same if it doesn't have any pure root then it's z=a+bi, right?:)