If $|z| = 1$, express $\overline{z}$ as a simplified fraction in terms of $z$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $|z| = 1$, express $\overline{z}$ as a simplified fraction in terms of $z$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1}{z}
If $|z| = 1$, express $\overline{z}$ as a simplified fraction in terms of $z$.
train