Classification of table algebras with two basis elements whose product is a linear combination of their conjugates

Table Algebras (A, B) with distinct non-real basis elements a, b is an element of B satisfying ab = m (a) over bar + n (b) over bar (m, n is an element of R+) are studied in this paper. The two cases where either a is real and b is non-real or a, b are both real were completely classified by Arad and Blau. Here, we study the remaining case where a and b are non-real.