On complex hybrid numbers: Algebraic structures, matrix representations, and geometric interpretations

This work introduces complex hybrid numbers, an extension of hybrid numbers, which are defined as Z = z0 + z1i + z2ɛ + z3ℎ where zi are complex numbers and iℎ = −ℎi = i + ɛ. We investigate their algebraic properties, classify them into ℂ1, ℂ2, D, and ℙ-types, and analyze their matrix representations. Numerical examples illustrate key findings, highlighting both their theoretical structure and potential areas of application. Key findings are demonstrated with numerical examples, emphasizing their structural importance and their uses.