Use the hint

The solution does not use the hint. It should include something to the effect of:

$\frac{z}{w}=z\cdot \frac{1}{w}=z\cdot \frac{\overline{w}}{w\overline{w}}=\frac{z\overline{w}}{|w{|}^2}.$

Thanks for pointing it out. It's corrected.