Q. The complex numbers sin $x + i\cos{2x\ and\cos{x - i\sin{2x}}\ }$are conjugate to each other for
A) $x = n\pi$
B) $x = \left( n + \frac{1}{2} \right)\pi$
C) $x = 0$
D) No value of $x$
Explanation
(d)
Let $(\cos{x - i\sin{2x) = \sin{x + i\cos{2x}}}}$
$\Rightarrow \ \cos{x + i\sin{2x = \sin{x + i\cos{2x}}}}$
$\therefore\ \cos{x = \sin{x\ \ and\ \sin{2x = \cos{2x}}}}$
$\Rightarrow \ \tan{x = 1\ \ and\ \tan{2x = 1}}$
Which is impossible
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.