Let F=(Z₃[x])/<x²+1>

Calculate (x + 1)⁴ in F. Explain why your calculation shows that F* is cyclic

I have calculated (x + 1)⁴and then divided the result by x^2+1 which gives me x+2

I am not sure if i have done this correctly and i dont see how this shows me that the multiplicative group will be cyclic.