Trigonometry (10th Edition)

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

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.3 The Product and Quotient Theorems - 8.3 Exercises - Page 369: 4

Answer

$-10\sqrt 3+10i$

Work Step by Step

$[4(\cos30^{\circ}+i\sin30^{\circ})][5(\cos120^{\circ}+i\sin120^{\circ}]$ Using the product theorem, the expression becomes $4(5)[\cos(30^{\circ}+120^{\circ})+i\sin(30^{\circ}+120^{\circ})]$ Simplifying, $20(\cos150^{\circ}+i\sin150^{\circ})$ We know that $\cos150^{\circ}=-\frac{\sqrt 3}{2}$ and $\sin150^{\circ}=\frac{1}{2}$ Substituting these values in the expression, $20(-\frac{\sqrt 3}{2}+\frac{1}{2}i)$ Therefore, the final answer is $-10\sqrt 3+10i$
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