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Question

For what value of x, the complex numbers sinx+icos2x and cosx-isin2x are conjugate to each other.


A

x=npi

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B

x=n+12pi

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C

x=0

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D

No values of x

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Solution

The correct option is D

No values of x


Determining the value ofx by using the conjugate relation:

Two complex numbers will only be conjugate, if their imaginary parts differ by their sign.

Given, sinx+icos2x is conjugate of cosx-isin2x.

That leads to. sinx-icos2x= cosx-isin2x

Comparing real and imaginary parts separately,

sinx=cosx(1)-cos2x=-sin2x(2)

From equation (1), we get,

tanx=1

From equation (2) we get,

tan2x=12tanx1-tan2x=1

Not satisfied by tanx=1

Hence, no values of x is possible.

Thus, the correct answer is option (D).


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