# Congruency grows complex

**Number Theory**Level 5

If you consider the Gaussian integers \(\mathbb{Z}[i]\) modulo \(2+i\), how many congruency classes are there?

**Clarifications**:

Gaussian integers are of the form \(a+bi\) where \(a\) and \(b\) are integers.

\(z_1\equiv z_2 \pmod{2+i}\) means that \(z_1-z_2=(2+i)w\) for some Gaussian integer \(w\).

**Bonus Question**: How many of the congruency classes are units, meaning that they have a multiplicative inverse?