Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.4 De Moivre's Theorem: Powers and Roots of Complex Numbers - 8.4 Exercises - Page 376: 32


$[{cis 60^{\circ},cis 180^{\circ},cis 300^{\circ}}]$

Work Step by Step

Given: $x^{3}+1=0$ or $x^{3}=-1$ $-1$ can be written in trigonometric form as: $-1=-1+0.i=1(\cos 180^{\circ}+\sin 180^{\circ})$ Absolute value of third root is given as $\sqrt[3] 1=1$ Now, the arguments can be given as: $k=0,1,2$ Roots: $1(\cos 60^{\circ}+\sin 60^{\circ})$,$1(\cos 180^{\circ}+\sin 180^{\circ})$,$1(\cos 300^{\circ}+\sin 300^{\circ})$ Solution set of the equation can be written as: $[{cis 60^{\circ},cis 180^{\circ},cis 300^{\circ}}]$
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