Trigonometry

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Complex, Quotient, Trigonometric, Standard, Conversion

TRIG-BHHICL

Given the two complex numbers:

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

Find $\cfrac { { z }_{ 1 } }{ { z }_{ 2 } } $, then convert your answer to standard form.

A

$\cfrac { { z }_{ 1 } }{ { z }_{ 2 } } =-\cfrac { 3 }{ 2 } i$

B

$\cfrac { { z }_{ 1 } }{ { z }_{ 2 } } =-\cfrac { 3 }{ 2 } $

C

$\cfrac { { z }_{ 1 } }{ { z }_{ 2 } } =\cfrac { 3 }{ 2 } +\cfrac { 3 }{ 2 } i $

D

$\cfrac { { z }_{ 1 } }{ { z }_{ 2 } } =\cfrac { 3 }{ 2 } i$