Trigonometry (10th Edition)

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

Chapter 8 - Quiz (Sections 8.1-8.4): 7c

Answer

$z^3$ = $- 23.38 + 13.50i$ (corr. to 2 decimal places)

Work Step by Step

$z = 3(cos50^\circ + isin50^\circ) = 3cis50^\circ$ Now, $z^3$ = $(3cis50^\circ)^3$ = $3^3 cis 3\cdot 50^\circ$ (De Moivre’s Theorem) = $27cis150^\circ$ = $27(cos150^\circ + isin150^\circ)$ = $27(-\frac{\sqrt{3}}{2} + \frac{1}{2} i)$ = $-\frac{27\sqrt{3}}{2} + \frac{27}{2}i$ = $- 23.38 + 13.50i$ (corr. to 2 decimal places)
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