Q. The value of $\frac{\cos{30{^\circ} + i\sin{30{^\circ}}}}{\cos{60{^\circ} - i\sin{60{^\circ}}}}$ is equal to
A) $i$
B) $- i$
C) $\frac{1 + \sqrt{3}i}{2}$
D) $\frac{1 - \sqrt{3}i}{2}$
Explanation
(a)
$\frac{\cos{30{^\circ} + i\sin{30{^\circ}}}}{\cos{60{^\circ} - i\sin{60{^\circ}}}}$
$= \left( \cos{30{^\circ} + i\sin{30{^\circ}}} \right)(\cos{60{^\circ} + i\sin{60{^\circ}}})$
$= \cos{90{^\circ} + i\sin{90{^\circ} = i}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.