Solve the Problem $\mathrm { I }$ In a Circuit with Voltage

Multiple Choice

Solve the problem.
-The current $\mathrm { I }$ in a circuit with voltage $\mathrm { E }$ , resistance $\mathrm { R }$ , capacitive reactance $X _ { \mathrm { C } }$ and inductive reactance $X _ { L }$ is
$$I = \frac { E } { R + \left( X _ { L } - X _ { C } \right) i }$$
Find $\mathrm { I }$ if $\mathrm { E } = 2 \sqrt { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) , \mathrm { R } = 4 , \mathrm { X } _ { \mathrm { L } } = 8$ , and $\mathrm { X } _ { \mathrm { C } } = 6$
Give your answer in rectangular form.

A) $\frac { 1 } { 5 } + \frac { 1 } { 5 } \mathrm { i }$
B) $\frac { 1 } { 5 } + \frac { 3 } { 5 } \mathrm { i }$
C) $\frac { 3 } { 5 } + \frac { 3 } { 5 } \mathrm { i }$
D) $\frac { 3 } { 5 } + \frac { 1 } { 5 } \mathrm { i }$