sinx + i cos2x and cos x – i sin 2x are conjugate to each other for:

Given that sin x + i cos 2x and cos x – i sin 2x are conjugate to each other.

⇒ sin x - i cos 2x = cos x – i sin 2x

On comparing real and imaginary parts of both sides, we get

⇒ sin x = cos x and cos 2x = sin 2x

⇒ tan x = 1 and tan 2x = 1

Consider tan 2x = 1

We know that

This is not satisfied by tan x = 1.

Hence, no value of x is possible.