Question

The complex number sin x+i cos 2x and cos x - i sin 2x are conjugate to each other for :

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

If sin x + icos 2x and cos x —sin 2x are conjugate to

each other, then (sin x+ icos 2x) =cos x - isin 2x
$\Rightarrow$ sin x - icos 2x = cos x - isin 2x

$\Rightarrow$ sin x = cos x and cos 2x = sin 2x

$\Rightarrow$ tan x =1 and tan 2x =1

Both these equations cannot hold simultaneously. Hence the correct answer is (d).