Answer
$\frac{z}{w}=\frac{2}{3}(\cos({53^\circ)}+i\sin{53^\circ}))$.
Work Step by Step
We know that if $z=a(\cos{\alpha}+i\sin{\alpha})$ and $w=b(\cos{\beta}+i\sin{\beta})$, then
$zw=ab(\cos({\alpha+\beta)}+i\sin{(\alpha+\beta})$ and
$\frac{z}{w}=\frac{a}{b}(\cos({\alpha-\beta)}+i\sin{(\alpha-\beta})$.
Hence here:
$\frac{z}{w}=\frac{2}{3}(\cos({85^\circ-22^\circ)}+i\sin({85^\circ-22^\circ}))\\\frac{z}{w}=\frac{2}{3}(\cos({53^\circ)}+i\sin{53^\circ}))$.
