Perform the operation shown below and leave the result in trigonometric form.
$$\frac { 36 ( \cos 2.5 + i \sin 2.5 ) } { 6 ( \cos 1.7 + i \sin 1.7 ) }$$
A) $6 ( \cos 0.8 + i \sin 0.8 )$
B) $30 ( \cos 0.8 + i \sin 0.8 )$
C) $30 ( \cos 1.5 + i \sin 1.5 )$
D) $6 ( \cos 4.2 + i \sin 4.2 )$
E) $6 ( \cos 4.25 + i \sin 4.25 )$

Question

Quizplus · Accepted Answer

The division of two complex numbers in trigonometric form, $\frac{r_1(\cos \theta_1 + i\sin \theta_1)}{r_2(\cos \theta_2 + i\sin \theta_2)}$, simplifies to $r(\cos(\theta_1 - \theta_2) + i\sin(\theta_1 - \theta_2))$ where $r = \frac{r_1}{r_2}$. Here, $r_1 = 36$, $r_2 = 6$, $\theta_1 = 2.5$, and $\theta_2 = 1.7$. Thus, $r = \frac{36}{6} = 6$ and $\theta = 2.5 - 1.7 = 0.8$, resulting in $6(\cos 0.8 + i\sin 0.8)$.

Perform the Operation Shown Below and Leave the Result in Trigonometric