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In the present paper, a new proposed theoretical hyper-complex chaotic system is proposed, which is an extension for the complex Lü models. In the proposed model, the variables, x, and y are assumed to be functions for one real and three complex parameters, while, the z variable is assumed in terms of only real variable only. After long mathematical manipulations, a systems of nine equations are obtained which represents the hyper-complex chaotic system. The dynamics of the obtained system were analyzed theoretically herein, where symmetry, anti-symmetry, Invariance, and dissipation of the system are theoretically analyzed from mathematical point of view. The paper will followed by a generalized paper for the same proposed model to check its applicability on the secure communication systems.