Find the product or quotient, as indicated. Leave your answer in polar form.
-Find the quotient.
$$\frac { 9 ( \cos 7 \pi + i \sin 7 \pi ) } { 4 ( \cos 5 \pi + i \sin 5 \pi ) }$$
A) $5 ( \cos 2 \pi + i \sin 2 \pi )$
B) $5 \left( \cos \frac { 7 } { 5 } + i \sin \frac { 7 } { 5 } \right)$
C) $\frac { 9 } { 4 } ( \cos 2 \pi + i \sin 2 \pi )$
D) $\frac { 9 } { 4 } \left( \cos \frac { 7 } { 5 } + i \sin \frac { 7 } { 5 } \right)$

Question

Quizplus · Accepted Answer

The quotient of two complex numbers in polar form is found by dividing their magnitudes and subtracting their angles. Here, the magnitude of the numerator is 9 and that of the denominator is 4, so the magnitude of the quotient is $9/4$. The angle of the numerator is $7\pi$ and that of the denominator is $5\pi$, so the angle of the quotient is $7\pi - 5\pi = 2\pi$. Therefore, the quotient in polar form is $\frac{9}{4}(\cos 2\pi + i\sin 2\pi)$.

Find the Product or Quotient, as Indicated 9(cos⁡7π+isin⁡7π)4(cos⁡5π+isin⁡5π)\frac { 9 ( \cos 7 \pi + i \sin 7 \pi ) } { 4 ( \cos 5 \pi + i \sin 5 \pi ) }4(cos5π+isin5π)9(cos7π+isin7π)​

Find the Product or Quotient, as Indicated $\frac { 9 ( \cos 7 \pi + i \sin 7 \pi ) } { 4 ( \cos 5 \pi + i \sin 5 \pi ) }$