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

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.