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Let z=sinx+icos2x and ω=cosx-isin2x. Then for what values of x are z and ω conjugate of each other?

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Let z=sinx+icos2x and ω=cosx-isin2x. Then for what values of x are z and ω conjugate of each other?

(a) x = nπ

(b) x = 0

(c) x = (n+1/2)π

(d) no value of x

I had been asked this question during an interview.

Enquiry is from Complex Conjugates in chapter Complex Numbers of Engineering Mathematics

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The correct answer is (d) no value of x

To explain: z̅=ω

∴ sinx=cosx and cos2x=sin2x

This is not possible for any value of x.

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