Multiply the complex numbers below and leave the result in trigonometric form. $$\left[ 7 \left( \cos \frac { 6 \pi } { 7 } + i \sin \frac { 6 \pi } { 7 } \right) \right] \left[ 2 \left( \cos \frac { 4 \pi } { 9 } + i \sin \frac { 4 \pi } { 9 } \right) \right]$$
A) $$9 \left( \cos \frac { 82 \pi } { 63 } + i \sin \frac { 82 \pi } { 63 } \right)$$
B) $$9 \left( \cos \frac { 10 \pi } { 63 } + i \sin \frac { 10 \pi } { 63 } \right)$$
C) $14 \left( \cos \frac { 10 \pi } { 63 } + i \sin \frac { 10 \pi } { 63 } \right)$
D) $14 \left( \cos \frac { 82 \pi } { 63 } + i \sin \frac { 82 \pi } { 63 } \right)$
E) $14 \left( \cos \frac { 58 \pi } { 63 } + i \sin \frac { 58 \pi } { 63 } \right)$

Question

Quizplus · Accepted Answer

When multiplying complex numbers in trigonometric form, you multiply the magnitudes and add the angles. Here, the magnitudes are 7 and 2, so their product is 14. The angles are $6\pi/7$ and $4\pi/9$, so their sum is $(54\pi + 28\pi)/63 = 82\pi/63$. Therefore, the correct answer is $14(\cos(82\pi/63) + i\sin(82\pi/63))$.

Multiply the Complex Numbers Below and Leave the Result in Trigonometric