# Prime and Irreducible in Z[i]

Assume that $a = bc$ then $N(a) = N(b)N(c)$ if $N(a)$ is prime then one of $N(b)$ or $N(c)$ is $1$ since the norm is $1$ it means the element is a unit. And so $b$ or $c$ is a unit. Thus $a$ is irreducible.