Perform the operation and leave the result in trigonometric form. $$\frac { 2 \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right) } { 4 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) }$$
A) $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
B) $\frac { 1 } { 2 } \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
C) $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } - i \sin 30 ^ { \circ } \right)$
D) $\frac { 1 } { 2 } \left( \cos 70 ^ { \circ } - i \sin 70 ^ { \circ } \right)$
E) $\frac { 1 } { 2 } \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right)$

Question

Perform the operation and leave the result in trigonometric form.​ $$\frac { 2 \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right) } { 4 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) }$$ ​
A)​ $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
B)​ $\frac { 1 } { 2 } \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
C)​ $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } - i \sin 30 ^ { \circ } \right)$
D)​ $\frac { 1 } { 2 } \left( \cos 70 ^ { \circ } - i \sin 70 ^ { \circ } \right)$
E)​ $\frac { 1 } { 2 } \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right)$

Quizplus · Accepted Answer

The division of complex numbers in trigonometric form is performed by dividing the magnitudes and subtracting the angles. Here, the magnitudes are $2/4 = 1/2$, and the angle difference is $70^\circ - 40^\circ = 30^\circ$, resulting in $\frac{1}{2}(\cos 30^\circ + i\sin 30^\circ)$.

Perform the Operation and Leave the Result in Trigonometric Form 2(cos⁡70∘+isin⁡70∘)4(cos⁡40∘+isin⁡40∘)\frac { 2 \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right) } { 4 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) }4(cos40∘+isin40∘)2(cos70∘+isin70∘)​

Perform the Operation and Leave the Result in Trigonometric Form $\frac { 2 \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right) } { 4 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right) }$