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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 $ E=6\sqrt { 2 } \left\{ \cos { \left( \cfrac { 5\pi }{ 6 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 6 } \right) } \right\}$ and $ I=3\sqrt { 2 } \left\{ \cos { \left( \cfrac { 5\pi }{ 12 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 12 } \right) } \right\},$ what is the impedance $Z$ ?

A

$Z=2\left\{ \cos { \left( \cfrac { 5\pi }{ 12 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 12 } \right) } \right\}$

B

$Z=2\left\{ \cos { \left( \cfrac { 5\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 4 } \right) } \right\}$

C

$Z=36\left\{ \cos { \left( \cfrac { 5\pi }{ 12 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 12 } \right) } \right\}$

D

$ Z=36\left\{ \cos { \left( \cfrac { 5\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 4 } \right) } \right\}$

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