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Neutrosophic complex numbers are a novel interesting generalization of classical complex numbers. This study aims to study the neutrosophic complex infinite rings, where we classify those rings as direct products by using classical complex field C. Also, this work introduces full solutions for 18 Kandasamy–Smarandache open problems concerning these structures, as well as the group of unit’s famous problem, where the group of units (invertible elements) of a neutrosophic complex ring will be classified as a direct product of two classical groups of units.