Answer
$zw=8\left(\cos{60^\circ}+i\sin{60^\circ}\right)$
and
$\dfrac{z}{w}=\dfrac{1}{2}\left(\cos{20^\circ}+i\sin{20^\circ}\right)$
Work Step by Step
Let us consider two complex numbers $z=a(\cos{\alpha}+i\sin{\alpha})$ and $w=b(\cos{\beta}+i\sin{\beta})$
Their product and quotient can be expressed as:
$zw=ab(\cos({\alpha+\beta)}+i\sin{(\alpha+\beta})$
$\dfrac{z}{w}=\dfrac{a}{b}[\cos({\alpha-\beta)}+i\sin{(\alpha-\beta}]$
Therefore,
$zw=(2 \cdot4)(\cos({40^\circ+20^\circ)}+i\sin{(40^\circ+20^\circ})]\\
zw=8\left(\cos{60^\circ}+i\sin{60^\circ}\right)$
and
$\dfrac{z}{w}=\dfrac{2}{4}\left[\cos{(40^\circ-20^\circ)}+i\sin{(40^\circ-20^\circ})\right]\\$
$\dfrac{z}{w}=\dfrac{1}{2}\left(\cos{20^\circ}+i\sin{20^\circ}\right)$
