Answer
$zw= \cos{220^\circ}+i\sin{220^\circ}$
$\dfrac{z}{w}=\cos{20^\circ}+i\sin{20^\circ}$
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:
$zw=ab(\cos({\alpha+\beta)}+i\sin{(\alpha+\beta})$ and
$\dfrac{z}{w}=\dfrac{a}{b}[\cos({\alpha-\beta)}+i\sin{(\alpha-\beta}]$
Therefore, in the given $z$ and $w$:
$zw=(1 \cdot 1)\left[\cos({120^\circ+100^\circ)}+i\sin ({120^\circ+100^\circ)}\right]\\
zw= \cos{220^\circ}+i\sin{220^\circ}$
and
$\dfrac{z}{w}=\dfrac{1}{1}\left[(\cos
{(120^\circ-100^\circ)}+i\sin{(120^\circ-100^\circ})\right]\\$
$\dfrac{z}{w}=\cos{20^\circ}+i\sin{20^\circ}$
