On Conjugates and Algebraic Forms of Bicomplex Numbers: Structures and Relationships

This paper investigates the structure of bicomplex numbers, with an emphasis on various types of conjugates, algebraic operations between those conjugates, and representation of conjugates in three forms: real, complex, and idempotent. We explore the behaviour and nature of the conjugates of a bicomplex number. We also deal with the similarities and differences between the conjugates of the idempotent components of a bicomplex number and the idempotent components of its conjugates, supported by relevant examples, theorems, and remarks.