Trigonometry (11th Edition) Clone

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

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.3 The Product and Quotient Theorems - 8.3 Exercises - Page 377: 41


$I = 1.185-0.136~i$

Work Step by Step

$I = \frac{E}{Z}$ $I = \frac{8~(cos~20^{\circ}+i~sin~20^{\circ})}{R+X_L~i}$ $I = \frac{8~(cos~20^{\circ}+i~sin~20^{\circ})}{6+3~i}$ $I = \frac{8~(cos~20^{\circ}+i~sin~20^{\circ})}{6+3~i}~\times~\frac{6-3~i}{6-3~i}$ $I = \frac{8~(6~cos~20^{\circ}+3~sin~20^{\circ}+i~6~sin~20^{\circ}-i~3~cos~20^{\circ})}{45}$ $I = \frac{8~(6.664216-0.766957~i)}{45}$ $I = 1.185-0.136~i$
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