I'm struggling to find the complex roots of $x^6-9x^3+8 = 0$. I've managed to find the real roots (1 and 2) by letting a variable, say $α = x^3$ and substituting where relevant, leading to a quadratic equation which I subsequently solved by factorization. I know this method is not at all helpful in finding complex roots though. :(
I would appreciate it if you could point me to the simplest way of finding the complex roots of this specific equation.