Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-$\frac { 50 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) } { 10 \left( \cos 32 ^ { \circ } + i \sin 32 ^ { \circ } \right) }$
A) $- 2.3474 + 4.4147 \mathrm { i }$
B) $4.4147 - 2.3474 \mathrm { i }$
C) $- 49.0976 + 9.4565 \mathrm { i }$
D) $9.4565 - 49.0976 \mathrm { i }$

Question

Quizplus · Accepted Answer

This problem involves complex numbers in polar form. The division of two complex numbers in polar form can be simplified using the formula $\frac{r_1(\cos \theta_1 + i\sin \theta_1)}{r_2(\cos \theta_2 + i\sin \theta_2)} = \frac{r_1}{r_2}(\cos(\theta_1 - \theta_2) + i\sin(\theta_1 - \theta_2))$. Here, $r_1 = 50$, $r_2 = 10$, $\theta_1 = 150^\circ$, and $\theta_2 = 32^\circ$. Thus, the division simplifies to $5(\cos(150^\circ - 32^\circ) + i\sin(150^\circ - 32^\circ))$. Calculating the cosine and sine of $118^\circ$ and multiplying by 5 gives the result $-2.3474 + 4.4147i$.

Perform the Indicated Operation 50(cos⁡150∘+isin⁡150∘)10(cos⁡32∘+isin⁡32∘)\frac { 50 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) } { 10 \left( \cos 32 ^ { \circ } + i \sin 32 ^ { \circ } \right) }10(cos32∘+isin32∘)50(cos150∘+isin150∘)​

Perform the Indicated Operation $\frac { 50 \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right) } { 10 \left( \cos 32 ^ { \circ } + i \sin 32 ^ { \circ } \right) }$