Question

The complex numbers $\sin x+i\cos 2x\&\cos x-i\sin 2x$ are conjugate to each other, for $x=$

• A. $n\pi$
• B. $\left(n+\frac{1}{2}\right)\pi$
• C. 0
• D. no value

Answer 1

Answer: (D)

$z_1={\overline{z}}_1$
$\sin x+i\cos 2x=\cos x+i\sin 2x\Rightarrow \sin x=\cos x\text{ and }\sin 2x=\cos 2x$
which is not possible