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

$I = 1.185-0.136~i$

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