Can someone check this for me?

[omega16]

Find the prime factorization of 6 in Q[sqrt(-1)].

Ans : Since 6 = 2*3
so 6 = (1+sqrt(-1)) (1-sqrt(-1)) *3 Q.E.D.

Do I need to add anything to it? Am I done with this question? Please kindly advise me. Thank you very much.

 

[StatusX]

How do you know those are prime?

 

[omega16]

because 2 and 3 are prime.

 

[StatusX]

I mean 1+sqrt(-1), 1-sqrt(-1), and 3 in the field Q(sqrt(-1)).