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Our paper is an attempt to to verify the Chen's conjecture on biharmonicsubmanifolds and to classify biconservative submanifolds.  In doing so we provide an affirmative answer to Chen's conjecture onbiharmonic submanifolds. We prove that every biconservative Lorentzhypersurface $M_{1}^{n}$ in $\mathbb{E}_{1}^{n+1}$ having complex eigenvalueshas constant mean curvature. Moreover, every biharmonic Lorentz hypersurface$M_{1}^{n}$ having complex eigenvalues in $\mathbb{E}_{1}^{n+1}$ must beminimal.

Biconservative Lorentz hypersurfaces in $\mathbb{E}_{1}^{\lowercase{n}+1}$ with complex eigenvalues