Q.

The complex numbers sinx+icos2x and cosx−isin2x  are conjugate to each other, for

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a

x=nπ

b

x=0

c

x=(n+1/2)π

d

no value of x

answer is D.

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Detailed Solution

Since, (sinx+icos2x¯)=cosx−isin2x ⇒                    sinx−icos2x=cosx−isin2x ⇒       sinx=cosx   and  cos2x=sin2x ⇒   tanx=1    and   tan2x=1 ⇒          x=π/4   and  x=π/8 which is not possible at same time. Hence, no solution exists.
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