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  4. The complex numbers sin x+i cos 2 x cos x-i sin 2 x are conjugate to each other, for x=

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

Complex Numbers and Quadratic Equations

Solution:

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