Q. The value of $\frac{4(\cos{75{^\circ} + i\sin{75{^\circ})}}}{0.4(\cos{30{^\circ} + i\sin{30{^\circ})}}}$ is
A) $\frac{\sqrt{2}}{10}(1 + i)$
B) $\frac{\sqrt{2}}{10}(1 - i)$
C) $\frac{10}{\sqrt{2}}(1 - i)$
D) $\frac{10}{\sqrt{2}}(1 + i)$
Explanation
(d)
$\frac{4(\cos{75{^\circ} + i\sin{75{^\circ})}}}{0.4(\cos{30{^\circ} + i\sin{30{^\circ})}}}$
$= 10(\cos{75{^\circ} + i\sin{75{^\circ})}}(\cos{30{^\circ} + i\sin{30{^\circ})}}$
$= 10\ e^{75i}.e^{- 30i} = 10e^{45i}$
$= 10(\cos{45{^\circ} + i\sin{45{^\circ}) = \frac{10}{\sqrt{2}}(1 + i)}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.