Divide the complex numbers below and leave the result in trigonometric form. $\frac { 2 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right) } { 9 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right) }$
A) $\frac { 2 } { 9 } \left( \cos 360 ^ { \circ } + i \sin 360 ^ { \circ } \right)$
B) $\frac { 2 } { 9 } \left( \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)$
C) $\frac { 2 } { 9 } \left( \cos 360 ^ { \circ } + i \sin 20 ^ { \circ } \right)$
D) $18 \left( \cos 360 ^ { \circ } + i \sin 360 ^ { \circ } \right)$
E) $18 \left( \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The division of the complex numbers results in simplification of the trigonometric parts, leaving the ratio of the coefficients, $ \frac{2}{9} $, with the angle unchanged. Since $ \cos 360^\circ = 1 $ and $ \sin 360^\circ = 0 $, the result is in the correct trigonometric form.

Divide the Complex Numbers Below and Leave the Result in Trigonometric