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in Complex Numbers by (50.2k points)
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sinx + i cos2x and cos x – i sin 2x are conjugate to each other for: 

A. x = nπ

B. x = (n + 1/2) π/2

C. x = 0 

D. No value of x

1 Answer

+1 vote
by (48.8k points)
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Best answer

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

This is not satisfied by tan x = 1.

Hence, no value of x is possible.

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