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Given ${ z }_{ 1 }=-\sqrt { 2 } +i\sqrt { 2 }\;$ and ${ z }_{ 2 }=1+i\sqrt { 3 }$, find ${ z }_{ 1 }\times { z }_{ 2 }\;$ in trigonometric form.

A

$4\left\{ \cos { \left( \cfrac { \pi }{ 12 } \right) } +i\sin { \left( \cfrac { \pi }{ 12 } \right) } \right\}$

B

$4+0.02i$

C

$4\left\{ \cos { \left( \cfrac {7 \pi }{ 12 } \right) } +i\sin { \left( \cfrac {7 \pi }{ 12 } \right) } \right\}$

D

$4\left\{ \cos { \left( \cfrac {-7 \pi }{ 12 } \right) } +i\sin { \left( \cfrac {-7 \pi }{ 12 } \right) } \right\}$

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