Can someone check this for me?

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The prime factorization of 6 in the field Q[sqrt(-1)] is established as 6 = (1+sqrt(-1))(1-sqrt(-1)) * 3. The factors 1+sqrt(-1) and 1-sqrt(-1) are confirmed as prime elements within this field, alongside the integer 3. The discussion clarifies that 2 and 3 are prime numbers in the rational integers, while the other factors are prime in the context of Q[sqrt(-1)].

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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.
 
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How do you know those are prime?
 
because 2 and 3 are prime.
 
I mean 1+sqrt(-1), 1-sqrt(-1), and 3 in the field Q(sqrt(-1)).
 

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