Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Test - Page 412: 7c


$z^3 =4~\sqrt{3}+4~i$

Work Step by Step

$z^3 = [2~(cos~10^{\circ}+i~sin~10^{\circ})]^3$ $z^3 = 2^3~[cos~(3\times 10^{\circ})+i~sin~(3\times 10^{\circ})]$ $z^3 = 8~(cos~30^{\circ}+i~sin~30^{\circ})$ $z^3 = 8~(\frac{\sqrt{3}}{2}+\frac{i}{2})$ $z^3 =4~\sqrt{3}+4~i$
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