Difficult# Complex Numbers, Applications, Electricity, Product

TRIG-HFCNMB

In electrical terms, an alternating current, $I$, through an electric inductor uses the formula $I=\cfrac { E }{ Z }\;amperes$, where $E$ is considered the voltage, and $Z=R+i{ X }_{ L }$ is known as the impedance. Given that the current is:

- $I=5\left\{ \cos { \left( \cfrac { \pi }{ 6 } \right) } +i\sin { \left( \cfrac { \pi }{ 6 } \right) } \right\}$
- $R=4$
- ${ X }_{ L }=3$

What is the voltage in rectangular form? (round your answer to the nearest hundredth)