Precalculus (6th Edition)

Published by Pearson

Chapter 8 - Application of Trigonometry - 8.6 De Moivre's Theorem; Powers and Roots of Complex Numbers - 8.6 Exercises: 10

Answer

$8$

Work Step by Step

. De Moivre’s Theorem states that when $r (\cos\theta+i \sin\theta)$ is a complex number, and if $n$ is any real number, then the following relationship holds. $[ r (\cos\theta+i \sin\theta)]^{n}=[ r^{n} (\cos n\theta+i \sin n\theta)]$ In compact form, this is written $[ r cis\theta]^{n}=[ r^{n} (cis \theta)]$ $[2 (\cos 120^{\circ}+i \sin 120^{\circ})]^{3}=[ (8\cos 3\times 120^{\circ}+i \sin 3\times 120^{\circ})]$ $=[ 8(\cos 360^{\circ}+i \sin 360^{\circ})]$ $=8(1+i.0)$ $=8$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.