We show that the number of distinct non-parallel lines passing through two conjugates of an algebraic number α of degree d 3 is at most [d2/2] − d + 2, its conjugates being in general position if this number is attained. If, for instance, d 4 is even, then the conjugates of α ∈ Q of degree d are in general position if and only if α has 2 real conjugates, d − 2 complex conjugates, no three distinct conjugates of α lie on a line and any two lines that pass through two distinct conjugates of α are… CONTINUE READING