Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 8 - Application of Trigonometry - 8.5 Trigonometric (Polar) Form of Complex Numbers: Products and Quotients - 8.5 Exercises - Page 802: 88

Answer

$$ - \frac{3}{6} - \frac{{3\sqrt 3 }}{2}i$$

Work Step by Step

$$\eqalign{ & \frac{{16\operatorname{cis} {{310}^ \circ }}}{{8\operatorname{cis} {{70}^ \circ }}} \cr & {\text{Using the Quotient Theorem}} \cr & = \frac{{16}}{8}\operatorname{cis} \left( {{{310}^ \circ } - {{70}^ \circ }} \right) \cr & = 3\operatorname{cis} \left( {{{240}^ \circ }} \right) \cr & = 3\left( {\cos {{240}^ \circ } + i\sin {{240}^ \circ }} \right) \cr & {\text{Write in Rectangular form}} \cr & = 3\left( { - \frac{1}{2} - \frac{{\sqrt 3 }}{2}i} \right) \cr & = - \frac{3}{6} - \frac{{3\sqrt 3 }}{2}i \cr} $$
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