Could you help me to calculate the hochschild homology of the following chain complex: $0 \longleftarrow M \longleftarrow M\otimes Z[i] \longleftarrow M\otimes Z[i]\otimes Z[i]\longleftarrow $
where $Z[i]$ is Gaussian intgers and $M$ is $Z[i]$-module.
I know that $Z[i] \cong Z^2$ and hence i can rewrite the chain complex as following:
$0 \longleftarrow M \longleftarrow M\otimes Z^2 \longleftarrow M\otimes Z^2\otimes Z^2\longleftarrow $
and i know that $H_n = ker/Im$. However i am struggling to calculate $H_0$, $H_1$ and $H_2$.
any help please.