a) Show that $N(ZZ') = N(Z)N(Z')$ for all $Z, Z' \in \mathbb{H}$. b) Show that $S$ is a subgroup of $\mathbb{H}^\times$ and that $\frac{1}{\sqrt{N(Z)}}Z \in S$ for all $Z \in \mathbb{H}^\times$.
a) Show that $N(ZZ') = N(Z)N(Z')$ for all $Z, Z' \in \mathbb{H}$.\\
b) Show that $S$ is a subgroup of $\mathbb{H}^\times$ and that $\frac{1}{\sqrt{N(Z)}}Z \in S$ for all $Z \in \mathbb{H}^\times$.