Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 8 - Section 8.3 - Polar Form of Complex Numbers; De Moivre's Theorem - 8.3 Exercises - Page 610: 4

Answer

$n$. $4$, $2, -2, 2i, -2i$, $2$. See graph.

Work Step by Step

How many different nth roots does a nonzero complex number have? $n$. The number 16 has $4$ fourth roots. These roots are $2, -2, 2i, -2i$. In the complex plane these roots all lie on a circle of radius $2$. See graph.
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