 So "L"∗ is the set of all complex numbers of the form
for some "n" ≥ 0, where all the β"i" and α"i" are algebraic and every branch of the logarithm is considered.The statement of the strong four exponentials conjecture is then as follows.Let "x"1, "x"2, and "y"1, "y"2 be two pairs of complex numbers with each pair being linearly independent over the algebraic numbers, then at least one of the four numbers "x""i" "y""j" for 1 ≤ "i","j" ≤ 2 is not in "L"∗.