Trigonometry

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Moderate

Complex, Product, Trigonometric Form, Standard Form

TRIG-SYQBWA

Given $ { z }_{ 1 }=8\left[ \cos { \left( \cfrac { 3\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 3\pi }{ 4 } \right) } \right] \; \text{ and}\; { z }_{ 2 }=9\left[ \cos { \left( \cfrac { 7\pi }{ 12 } \right) } +i\sin { \left( \cfrac { 7\pi }{ 12 } \right) } \right]$

What is $ { z }_{ 1 }\times { z }_{ 2 }$? Write your answer in standard form.

A

$-36-36\sqrt { 3 }$

B

$-72-72\sqrt { 3 }$

C

$-24-24\sqrt { 2 }$

D

$-24-24\sqrt { 2 }$