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In this work we obtain the exact solution for relativistic Landau problemplus oscillator potential in a complex symmetric gauge field in anon-commutative complex space, using the algebraic techniques of creation andannihilation operators. It is shown that the relativistic Landau problem in acomplex symmetric gauge field in a non-commutative complex space is similarbehavior to the Pauli equation in the presence of a symmetric gauge field in acommutative ordinary space. We derive the exact non-commutative Landau andoscillator energy levels, while the non-relativistic limit of the energyspectrum is obtained. We show that the energy is not degenerate and is splittedinto two levels, as in the Zeeman effect.

Relativistic Landau and oscillator levels in a symmetric gauge field in a non-commutative complex space