Please don't solve the problem - it is for an assignment - this is just a question for clarification purposes.
Let $G$ be a group and $\hat G$ be the set of homomorphisms from $G$ to the group of non-zero complex numbers.
Q: Show that $\hat{Z/n}$ is a cyclic group of order $n$.
SubQ: Define a binary operation on $\hat G$ as follows: If $\alpha,\beta \in \hat G$ we let $\alpha \circ \beta $ be the function that maps $\alpha \circ \beta:g\mapsto \alpha(g) \beta(g) $
I have already done this part.
My question: Do they want to to show that the group of all homomorphisms as defined by the mapping above from $\Bbb Z / n\Bbb Z$ to $\Bbb C_{\ne 0}$, is a cyclic group itself and that this cyclic group has $n$ elements?