In the ring $\mathbb Z[i]$ explain why our four units $\pm1$ and $\pm i$ divide every $u\in\mathbb Z[i]$. In the ring $\mathbb Z[i]$ explain why our four units $\pm1$ and $\pm i$ divide every $u\in\mathbb Z[i]$.
This is obviously a elementary question, but Gaussian integers are relatively new to me.  I found this exercise in the textbook, and my professor overlooked it, but i'm curious.
Is this basically the same thing as, for a lack of a better term, "normal" integers?  As in, $\pm1$ divides everything?

Hint $\ $  Units $\rm\:u\mid 1\mid x.\ $ Alternatively $\rm\ u\mid u(u^{-1}x) = (uu^{-1})x = x$
