Roots of polynomial with imaginary coefficients

Question

This is the first time I see this kind of problem, so it might be trivial but I am just not used to it.

What are the roots of $x^3-6ix^2-11x+6i$

I am not sure If I should ignore the imaginary numbers and simply compute the polynomial or factor the imaginary part out separately.

I tried to use the rational polynomial root test but it has no rational roots when I ignore the Imaginary coefficients.

When I factor them out as $x^3-11x-i(6x^2-6)$ I get $i$ and $-i$ as a root which is definitely wrong.

All I ask for here is to provide me advice on what method should I use to solve this type of problems. Thanks in advance.

Answer 1

Hint:

$x=iy$

Now if $f(y)=y^3-6y^2+11y-6$

$f(1)=?$