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: 7b


$\frac{w}{z} = 2~\sqrt{3}+2~i$

Work Step by Step

$\frac{w}{z} = \frac{8~(cos~40^{\circ}+i~sin~40^{\circ})}{2~(cos~10^{\circ}+i~sin~10^{\circ})}$ $\frac{w}{z} = \frac{8}{2}~[cos~(40^{\circ}-10^{\circ})+i~(sin~40^{\circ}-10^{\circ})]$ $\frac{w}{z} = 4~(cos~30^{\circ}+i~sin~30^{\circ})$ $\frac{w}{z} = 4~(\frac{\sqrt{3}}{2}+\frac{i}{2})$ $\frac{w}{z} = 2~\sqrt{3}+2~i$
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