Answer
$-10\sqrt 3+10i$
Work Step by Step
$[4(\cos30^{\circ}+i\sin30^{\circ})][5(\cos120^{\circ}+i\sin120^{\circ}]$
Using the product theorem, the expression becomes
$4(5)[\cos(30^{\circ}+120^{\circ})+i\sin(30^{\circ}+120^{\circ})]$
Simplifying, $20(\cos150^{\circ}+i\sin150^{\circ})$
We know that $\cos150^{\circ}=-\frac{\sqrt 3}{2}$ and $\sin150^{\circ}=\frac{1}{2}$
Substituting these values in the expression, $20(-\frac{\sqrt 3}{2}+\frac{1}{2}i)$
Therefore, the final answer is $-10\sqrt 3+10i$