Perform the operation shown below and leave the result in trigonometric form.
$$\left[ 6 \left( \cos 90 ^ { \circ } + i \sin 90 ^ { \circ } \right) \right] \left[ 2 \left( \cos 280 ^ { \circ } + i \sin 280 ^ { \circ } \right) \right]$$
A) $8 \left( \cos 370 ^ { \circ } + i \sin 370 ^ { \circ } \right)$
B) $12 \left( \cos 252 ^ { \circ } + i \sin 252 ^ { \circ } \right)$
C) $12 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)$
D) $8 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)$
E) $12 \left( \cos 370 ^ { \circ } + i \sin 370 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

Multiplying complex numbers in trigonometric form involves multiplying their magnitudes and adding their angles. Here, $6 \times 2 = 12$ and $90^\circ + 280^\circ = 370^\circ$. The result is in the form $r(\cos \theta + i\sin \theta)$, where $r = 12$ and $\theta = 370^\circ$.

Perform the Operation Shown Below and Leave the Result in Trigonometric