I know that $$ \mathcal{Z} \left\lbrace x_1[n] * x_2[n] \right\rbrace = X_1(z) X_2(z).$$
But what would $$ X_1(z+a) X_2(z+a) $$ be equal to in terms of $ x_1[n] $ and $ x_2[n] $? i.e. what does frequency-shifting do to the signals in this case?
I have that \begin{align} X_1(z+a)X_2(z+a) &= \sum_{n=-\infty}^{\infty} \left [\sum_{l=-\infty}^{\infty} x_1(l)x_2(n-l) \right ](z+a)^{-n}\\ &= \mathcal{Z} \left \{ ? \right \} \\ \end{align} but I am not sure where to go from here.