On the para-octonions; a non-associative normed algebra
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In this paper, para-octonions and their algebraic properties are provided by using the Cayley-Dickson multiplication rule between the octonionic basis elements. The trigonometric form of a para-octonion is similar to the trigonometric form of dual number and quasi-quaternion. We study the De-Moivre’s theorem for para-octonions, extending results obtained for real octonions and defining generalize Euler’s formula for para-octonions.