I know very little about group cohomology but the following came up in something else I was looking at: Let $c_1,c_2,\ldots,c_n \in \mathbb C$ and let $\mathbb Z^n$ act on $\mathbb C$ via the representation $\mathbb Z^n \ni (m_1,\ldots,m_n) \mapsto e^{m_1c_1 + \cdots + m_1 c_n} \in GL(1,\mathbb C)$. Then what is the group cohomology $H^i(\mathbb Z^n, \mathbb C)$?
I know how to do the case $n=1$. Maybe there is a way to reduce it to that case?
Thanks!