Question

If $|z|=3$, then $\frac{9+z}{1+\overline{z}}$ equals

• A. $z$
• B. $\overline{z}$
• C. $3z$
• D. $z+\overline{z}$

Answer 1

The correct option is A $z$

Given that, $|z|=3$
$\Rightarrow {\left|z\right|}^2=9$
$\Rightarrow z\overline{z}=9$
$\Rightarrow \overline{z}=\frac{9}{z}$
let $w=\frac{9+z}{1+\overline{z}}$
$\Rightarrow w=\frac{9+z}{1+\frac{9}{z}}=z$
Ans: A