# Congruency grows complex

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?

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