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Trigonometry

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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)

A

$9.82+22.99i$

B

$19.86+15.18i$

C

$2.99+24.82i$

D

$-9.82-22.99i$