# Chapter 6 - Section 6.7 - The Dot Product - Exercise Set - Page 799: 71

$4 +i 4 \sqrt 3$

#### 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 $[ 2 (\cos 20^{\circ}+i \sin 20^{\circ})]^3=4 +i 4 \sqrt 3$

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