# Math Help - Irreducible in Z[i]

1. ## Irreducible in Z[i]

Show that $1 - i$ is an irreducible in $Z[i]$.

Proof. Suppose that 1 - i = ab, for a and b in Z[i], we need to show that either a or b is a unit.

I'm having trouble trying to do this one, is there a certain factor that 1 - i has that can allow me to conclude the other has to be a unit?

Show that $1 - i$ is an irreducible in $Z[i]$.

Proof. Suppose that 1 - i = ab, for a and b in Z[i], we need to show that either a or b is a unit.

I'm having trouble trying to do this one, is there a certain factor that 1 - i has that can allow me to conclude the other has to be a unit?
Hint: $1+i = (a+ib)(x+iy)$ where $a,b,x,y\in \mathbb{Z}$. Now equate.

Show that $1 - i$ is an irreducible in $Z[i]$.