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The concept of unity roots plays a central role in the theory of field extensions and polynomials roots' computing. The objective of this paper is to find the algebraic formula for computing the symbolic 2-plithogenic and 3-plithogenic complex roots of unity, where a general formula will be provided with many related examples up to the exponent 3. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study for the first time the concept of square real matrices with symbolic 2-plithogenic split-complex entries. Many of their algebraic properties will be discussed and handled, where we find the formula of computing inverses, exponents, and powers of these matrices by building a ring isomorphism between the ring of split-complex symbolic 2-plithogenic matrices and the direct product of the symbolic 2-plithogenic matrices with itself. Also, we give the interested reader many related examples to clarify the validity of our work. [ABSTRACT FROM AUTHOR]

The goal of this paper is to define for the first time the concept of symbolic 2-plithogenic weak fuzzy complex number as new generalization generated by combining real numbers with symbolic 2-plithogenic numbers. We study the elementary properties of this new class such as Invertibility and nilpotency, with many related examples that explain its novelty. [ABSTRACT FROM AUTHOR]

Complex numbers have been studied in previous papers, but the papers did not deal with the conversion from algebraic form of a neutrosophic complex number form to exponential or trigonometric form and vice versa, and this prompted us to search for a method that facilitates this conversion process, as this paper dealt with how to move from algebraic form of a neutrosophic complex number to exponential or trigonometric form and vice versa, also, we discussed the roots from order n of a neutrosophic complex number, whether this number is given in algebraic or trigonometric form. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the neutrosophic complex finite rings C(Zn) and C(< Zn ∪ I >), and to give a classification theorem of these rings. Also, this work introduces full solutions for 12 Kandasamy-Smarandache open problems concerning these structures of generalized rings modulo integers. Also, a necessary and sufficient condition of invertibility in C(Zn) and C(< Zn ∪ I >) is presented as a partial solution of the famous group of units problem. [ABSTRACT FROM AUTHOR]