Ευκλείδειος Μιγαδική Σχετικιστική Μηχανική Ι: Ο Πίνακας (Greek title) Relativity Theory was fundamental for the development of Quantum Physics. These parts of Physics are applied to sections, such as Chemistry, Biology, Pharmacology and Medicine. As a result, a significant change on Relativity will lead to changes on the above scientific sections. Special Relativity, as is applied until now, cancels the transitive attribute in parallelism, when three observers are related, because Lorentz Transformation is not closed. In this paper, considering Linear Space-time Transformation, we demand the maintenance of Space-time distance S2. In addition, we demand this Transformation to be closed, so there is no need for axis rotation. The solution is a matrix containing complex numbers. As a result, space becomes complex, but time remains real. Thus, the transitive attribute in parallelism, which is equivalent to the Euclidean Request, is also valid for moving observers