Divide the complex numbers below and leave the result in trigonometric form. $\frac { 5 \left( \cos 100 ^ { \circ } + i \sin 100 ^ { \circ } \right) } { 9 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) }$
A) $\frac { 5 } { 9 } \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
B) $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$
C) $45 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
D) $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
E) $45 \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$

Question

Divide the complex numbers below and leave the result in trigonometric form. $\frac { 5 \left( \cos 100 ^ { \circ } + i \sin 100 ^ { \circ } \right) } { 9 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) }$  
A) $\frac { 5 } { 9 } \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
B)  $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$
C)  $45 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
D)  $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
E)  $45 \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$

Quizplus · Accepted Answer

When dividing complex numbers in trigonometric form, the magnitudes are divided and the angles are subtracted. Therefore, the result is $\frac{5}{9}(\cos(100^\circ - 120^\circ) + i\sin(100^\circ - 120^\circ)) = \frac{5}{9}(\cos(-20^\circ) + i\sin(-20^\circ))$, which simplifies to $\frac{5}{9}(\cos(340^\circ) + i\sin(340^\circ))$, since adding 360° to the angle doesn't change its direction.

Divide the Complex Numbers Below and Leave the Result in Trigonometric