Answer
$zw=12(cos40^\circ+i\ sin40^\circ), \frac{z}{w}=\frac{3}{4}(cos220^\circ+i\ sin220^\circ)$
Work Step by Step
Given $z=3(cos130^\circ+i\ sin130^\circ)$ and $w=4(cos270^\circ+i\ sin270^\circ)$, we have:
1. $zw=12(cos(130+270)^\circ+i\ sin(130+270)^\circ)=12(cos(360+40)^\circ+i\ sin(360+40)^\circ)=12(cos40^\circ+i\ sin40^\circ)$
2. $\frac{z}{w}=\frac{3}{4}(cos(130-270)^\circ+i\ sin(130-270)^\circ)=\frac{3}{4}(cos(-140)^\circ+i\ sin(-140)^\circ)=\frac{3}{4}(cos220^\circ+i\ sin220^\circ)$
