Cardinal of quotient rings of gaussian integers. It is known that $\mathbb{Z}[i]$ is a PID and that $\mathbb{Z}[i]/(a+bi)\mathbb{Z}[i]$ is finite for all $(a,b) \in \mathbb{Z}^2\backslash \{(0,0)\}$.
My question : 

Is there any result on the cardinal of  $\mathbb{Z}[i]/(a+bi)\mathbb{Z}[i]$ ? 


Here's a geometric solution: In the complex plane, consider the parallelogram with vertices at $0, a+bi, -b+ai$ and $a-b+(a+b)i$. Show that every point in $\mathbb{Z}[i]$ is congruent to some lattice point in this parallelogram modulo $a+bi$. Now count the number of lattice points that are in the parallelogram using Pick's Formula.
