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Trigonometry

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Moderate

Complex Numbers, Product, Trigonometric Form

TRIG-NYQSSL

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

$$\left[ 5\left( \cos { \cfrac { \pi }{ 4 } } \right) +\sin { \left( \cfrac { \pi }{ 4 } \right) } \right] \left[ 4\left( \cos { \left( \cfrac { \pi }{ 12 } \right) } +i\sin { \left( \cfrac { \pi }{ 12 } \right) } \right) \right]$$

A

$20\left[ \cos { \left( \cfrac { \pi }{ 3 } \right) } +i\sin { \left( \cfrac { \pi }{ 3 } \right) } \right]$

B

$ 20\left[ \cos { \left( \cfrac { { \pi }^{ 2 } }{ 48 } \right) } +i\sin { \left( \cfrac { { \pi }^{ 2 } }{ 48 } \right) } \right]$

C

$ 9\left[ \cos { \left( \cfrac { \pi }{ 12 } \right) } +i\sin { \left( \cfrac { \pi }{ 12 } \right) } \right]$

D

$ 9\left[ \cos { \left( \cfrac { { \pi }^{ 2 } }{ 48 } \right) } +i\sin { \left( \cfrac { { \pi }^{ 2 } }{ 48 } \right) } \right]$