Answer both questions with a minimum of 80 words per question:

1. I hope the notation Z[�] is for Z[
√
−1]. Now if in the ring we can define
Norm as follows
N(a + bi) = a2 + b2
with this norm this ring becomes Euclidean domain. In particular this
ring is PID and UFD.
Now p = a + bi is prime in Z[i] if and only if
1- Either a or b or zero and other is...