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Trigonometry

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Moderate

Complex Numbers, Product, Leave in Trigonometric Form

TRIG-N93LPH

Find the product of the two complex numbers and leave in trigonometric form.

$$\left[ 4\left( \cos { \cfrac { 5\pi }{ 6 } } \right) +\sin { \left( \cfrac { 5\pi }{ 6 } \right) } \right] \left[ 7\left( \cos { \left( \cfrac { 4\pi }{ 3 } \right) } +i\sin { \left( \cfrac { 4\pi }{ 3 } \right) } \right) \right]$$

A

$28\left[ \cos { \left( \cfrac { { 10\pi }^{ 2 } }{ 9 } \right) } +i\sin { \left( \cfrac { { { 10\pi }^{ 2 } } }{ 9 } \right) } \right]$

B

$11\left[ \cos { \left( \cfrac { 13\pi }{ 6 } \right) } +i\sin { \left( \cfrac { 13\pi }{ 6 } \right) } \right]$

C

$11\left[ \cos { \left( \cfrac { { 10\pi }^{ 2 } }{ 9 } \right) } +i\sin { \left( \cfrac { { { 10\pi }^{ 2 } } }{ 9 } \right) } \right]$

D

$28\left[ \cos { \left( \cfrac { 13\pi }{ 6 } \right) } +i\sin { \left( \cfrac { 13\pi }{ 6 } \right) } \right]$