Abstract
Today, the theory of hypercomplex numbers is a rapidly developing field of mathematical knowledge due to its numerous applications in various branches of physics. For example, dual numbers allow us to model the physical space-time quite accurately mathematically, quaternions are used in electrodynamics, in the study of vortex motions, octaves also represent a mathematical model of a possible description of our reality [1-6]. In the article [7], by analogy with the work [8] of the Iranian mathematicians X. Mortazashl and M. Jafari, who gave the concept of a semi-quaternion, the definition of semi-octaves and operations on them is introduced, as well as some properties of these operations are established. This work continues the research started in [7]. Definitions of the norm of semi-octaves and linear equations over semi-octaves are introduced here, formulas for solving such equations are found. Analogs of the Euler and Moivre formulas, which originally took place for complex numbers, are also established for semi-octaves.
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