Let $G= \{ z \in \mathbb{C} \ \ | \ \ az^{n}=b \}, a \in \mathbb{C^{\*}}, b \in \mathbb{C}$.

Find $a$ and $b$ such that $G$ is a subgroup of $(\mathbb{C^{\*}},\cdot)$ where $\cdot$ is the regular multiplication.

The answer should be $a=b$.