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If the complex numbers $sinx+icos2x$ and $cosx-isin2x$ are conjugate to each other, then $x=?$

(A) $x=0$ (B) $x=n\pi+\large\frac{\pi}{4}$ (C) $n\pi$ (D) No value of $ x$ exist
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  • $\overline {x+iy}=x-iy$
Given $\overline {sinx+icos2x}=cosx-isin2x$
$\Rightarrow\:sinx-icos2x=cosx-isin2x$
Comparing the Real and Imaginary parts on either sides
$sinx=cosx$ and $cos2x=sin2x$
$\Rightarrow\:tanx=1\:\:\:and\:\:\:tan2x=1$
$\Rightarrow\:x=n\pi +\large\frac{\pi}{4}$ $and$ $x=\large\frac{n\pi}{2}+\frac{\pi}{8}$
$x$ cannot be simultaneously equal to 2 different values.
$\therefore$ no value of $x$ exist
answered Jul 15, 2013 by rvidyagovindarajan_1
 

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