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

The operation simplifies to $\frac{1}{2}(\cos(110^\circ - 50^\circ) + i\sin(110^\circ - 50^\circ))$, which equals $\frac{1}{2}(\cos60^\circ + i\sin60^\circ)$.