Perform the operation shown below and leave the result in trigonometric form.
$\frac { 12 ( \cos 3.1 + i \sin 3.1 ) } { 6 ( \cos 2.7 + i \sin 2.7 ) }$
A) $6 ( \cos 0.4 + i \sin 0.4 )$
B) $6 ( \cos 1.1 + i \sin 1.1 )$
C) $2 ( \cos 0.4 + i \sin 0.4 )$
D) $2 ( \cos 8.37 + i \sin 8.37 )$
E) $2 ( \cos 5.8 + i \sin 5.8 )$

Question

Perform the operation shown below and leave the result in trigonometric form.  
  $\frac { 12 ( \cos 3.1 + i \sin 3.1 ) } { 6 ( \cos 2.7 + i \sin 2.7 ) }$
A) $6 ( \cos 0.4 + i \sin 0.4 )$
B)  $6 ( \cos 1.1 + i \sin 1.1 )$
C)  $2 ( \cos 0.4 + i \sin 0.4 )$
D)  $2 ( \cos 8.37 + i \sin 8.37 )$
E)  $2 ( \cos 5.8 + i \sin 5.8 )$

Quizplus · Accepted Answer

This problem involves dividing two complex numbers in trigonometric form. The formula for dividing complex numbers in trigonometric form is $\frac{r_1(\cos \theta_1 + i\sin \theta_1)}{r_2(\cos \theta_2 + i\sin \theta_2)} = \frac{r_1}{r_2}(\cos(\theta_1 - \theta_2) + i\sin(\theta_1 - \theta_2))$. Applying this formula, we get $\frac{12}{6}(\cos(3.1 - 2.7) + i\sin(3.1 - 2.7)) = 2(\cos 0.4 + i\sin 0.4)$.

Perform the Operation Shown Below and Leave the Result in Trigonometric