Abstract
This paper is dedicated to defining for the first time the concept of complex refined neutrosophic numbers as a direct application of refined neutrosophic sets and as a new generalization of neutrosophic complex numbers. Also, it presents some of their elementary properties such as conjugates, absolute values, invertibility, and algebraic operations. The importance of the definitions in this article lies in the use of them by defining the polar form of the refined neutrosophic complex numbers.
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