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In electronics a commonly used formula is,
$$ E\; =\; I\; \times \; Z$$

...where $ E\;$ is voltage, $ I\;$ is current, and $Z\;$ is impedance.

If $Z=\cfrac { \sqrt { 2 } }{ 2 } \left\{ \cos { \left( \cfrac { 3\pi }{ 2 } \right) } +i\sin { \left( \cfrac { 3\pi }{ 2 } \right) } \right\} $and$\;I=\cfrac { \sqrt { 3 } }{ 3 } \left\{ \cos { \left( \cfrac { 5\pi }{ 3 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 3 } \right) } \right\} ,$ what is the voltage $E$ ?

(Write your answer in standard form.)

A

$ E=\cfrac { \sqrt { 2 } }{ 4 } -\cfrac { \sqrt { 6 } }{ 12 } i$

B

$ E=-\cfrac { \sqrt { 6 } }{ 2 } -\cfrac { \sqrt { 6 } }{ 4 } i$

C

$ E=\cfrac { 3\sqrt { 2 } }{ 4 } -\cfrac { \sqrt { 6 } }{ 4 } i$

D

$ E=-\cfrac { \sqrt { 2 } }{ 4 } -\cfrac { \sqrt { 6 } }{ 12 } i$

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