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 the angle does not change and the complex numbers are identical in both numerator and denominator, the result is simply the coefficient ratio multiplied by the original trigonometric form, which simplifies to $\cos 360^\circ + i \sin 360^\circ$, equivalent to 1.

Divide the Complex Numbers Below and Leave the Result in Trigonometric