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Trigonometry

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Moderate

Complex Numbers, Trigonometric Form, Quotient, Radian

TRIG-RY7BUS

Given the two complex numbers:

$${ z }_{ 1 }=5\left[ \cos { \left( \cfrac { 5\pi }{ 3 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 3 } \right) } \right]$$
$${ z }_{ 2 }=2\left[ \cos { \left( \cfrac { 3\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 3\pi }{ 4 } \right) } \right]$$

What is $\cfrac { { z }_{ 1 } }{ { z }_{ 2 } }$?

Leave your answer in trigonometric form.

A

$\cfrac { 5 }{ 2 } \left[ \cos { \left( \cfrac { 11\pi }{ 12 } \right) } +i\sin { \left( \cfrac { 11\pi }{ 12 } \right) } \right]$

B

$\cfrac { 5 }{ 2 } \left[ \cos { \left( \cfrac { 29\pi }{ 12 } \right) } +i\sin { \left( \cfrac { 29\pi }{ 12 } \right) } \right]$

C

$\cfrac { 2 }{ 5 } \left[ \cos { \left( \cfrac { 11\pi }{ 12 } \right) } +i\sin { \left( \cfrac { 11\pi }{ 12 } \right) } \right]$

D

$\cfrac { 2 }{ 5 } \left[ \cos { \left( \cfrac { 29\pi }{ 12 } \right) } +i\sin { \left( \cfrac { 29\pi }{ 12 } \right) } \right]$