Perform the operation and leave the result in trigonometric form. $\frac { \left( \cos 110 ^ { \circ } + i \sin 110 ^ { \circ } \right) } { 2 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) }$
A) $\frac { 1 } { 2 } \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$
B) $\frac { 1 } { 2 } \left( \cos 60 ^ { \circ } - i \sin 60 ^ { \circ } \right)$
C) $\frac { 1 } { 2 } \left( \cos 110 ^ { \circ } + i \sin 110 ^ { \circ } \right)$
D) $\frac { 1 } { 2 } \left( \cos 110 ^ { \circ } - i \sin 110 ^ { \circ } \right)$
E) $\frac { 1 } { 2 } \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right)$

Question

Perform the operation and leave the result in trigonometric form.   $\frac { \left( \cos 110 ^ { \circ } + i \sin 110 ^ { \circ } \right) } { 2 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) }$  
A) $\frac { 1 } { 2 } \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$
B)  $\frac { 1 } { 2 } \left( \cos 60 ^ { \circ } - i \sin 60 ^ { \circ } \right)$
C)  $\frac { 1 } { 2 } \left( \cos 110 ^ { \circ } + i \sin 110 ^ { \circ } \right)$
D)  $\frac { 1 } { 2 } \left( \cos 110 ^ { \circ } - i \sin 110 ^ { \circ } \right)$
E)  $\frac { 1 } { 2 } \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right)$

Quizplus · Accepted Answer

This operation can be simplified using the formula for dividing complex numbers in trigonometric form: $\frac{\cos \theta + i\sin \theta}{\cos \phi + i\sin \phi} = \cos(\theta - \phi) + i\sin(\theta - \phi)$. Applying this to the given problem, we get $\cos(110^\circ - 50^\circ) + i\sin(110^\circ - 50^\circ) = \cos(60^\circ) + i\sin(60^\circ)$, and since it's divided by 2, the correct answer is $\frac{1}{2}(\cos 60^\circ + i\sin 60^\circ)$.