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Trigonometry

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Complex Numbers, Trigonometric Form, Quotient

TRIG-NW17FF

Given the two complex numbers:

$${ z }_{ 1 }=\cfrac { 5 }{ 6 } \left[ \cos { \left( \cfrac { 7\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 7\pi }{ 4 } \right) } \right]$$
$${ z }_{ 2 }=2\left[ \cos { \left( \cfrac { \pi }{ 2 } \right) } +i\sin { \left( \cfrac { \pi }{ 2 } \right) } \right]$$

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

A

$\cfrac { { z }_{ 1 } }{ { z }_{ 2 } }=\cfrac { 5 }{ 12 } \left[ \cos { \left( \cfrac { 9\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 9\pi }{ 4 } \right) } \right]$

B

$\cfrac { { z }_{ 1 } }{ { z }_{ 2 } }=\cfrac { 12 }{ 5 } \left[ \cos { \left( \cfrac { 5\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 4 } \right) } \right]$

C

$\cfrac { { z }_{ 1 } }{ { z }_{ 2 } }=\cfrac { 12 }{ 5 } \left[ \cos { \left( \cfrac { 9\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 9\pi }{ 4 } \right) } \right]$

D

$\cfrac { { z }_{ 1 } }{ { z }_{ 2 } }=\cfrac { 5 }{ 12 } \left[ \cos { \left( \cfrac { 5\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 5\pi }{ 4 } \right) } \right]$