Trigonometry

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Moderate

Complex Numbers, Trig Form, Standard Form, Product, Radian

TRIG-2YFWJS

Given the complex numbers:

$${ z }_{ 1 }=\cfrac { 3 }{ 2 } \left[ \cos { \left( \cfrac { 23\pi }{ 12 } \right) } +i\sin { \left( \cfrac { 23\pi }{ 12 } \right) } \right]$$
$${ z }_{ 2 }=6\left[ \cos { \left( \cfrac { -\pi }{ 4 } \right) } +i\sin { \left( \cfrac { -\pi }{ 4} \right) } \right]$$

What is their product? Write your answer in standard complex form. ($a+bi$)

A

$\cfrac { 9 }{ 2 } +\cfrac { 9\sqrt { 3 } }{ 2 }$

B

$\cfrac { 9 }{ 4 } +\cfrac { -9\sqrt { 3 } }{ 4 }$

C

$\cfrac { -9 }{ 2 } +\cfrac { -9\sqrt { 3 } }{ 2 } $

D

$\cfrac { 9 }{ 2 } +\cfrac { -9\sqrt { 3 } }{ 2 }$