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 ∈ B satisfying ab=3Dm‾a + n‾b, m,n ∈ R⁺, are studied in this paper. The two cases where either a is real and b is non-real or a,b are both reals were completely classified by Z. Arad and H. Blau. Here we study the remaining case where a and b are non-real.