Answer
$4 +i 4 \sqrt 3$
Work Step by Step
Given: $[ 2 (\cos 20^{\circ}+i \sin 20^{\circ})]^3=(2)^3 \times [ \cos (3 \times 20 +i \sin (3 \times 20)]$
$=8( \cos 60^{\circ} +i \sin 60^{\circ})$
$=8[ \dfrac{1}{2} +i \dfrac{\sqrt 3}{2}]$
Thus, we have $[ 2 (\cos 20^{\circ}+i \sin 20^{\circ})]^3=4 +i 4 \sqrt 3$
