For any complex number w = c + id, let arg(w) ∈ (−π, π], where i = √−1. Let α and β be real numbers such that for all complex numbers z = x + iy satisfying arg((z + α)/(z + β)) = π/4, the ordered pair (x, y) lies on the circle x² + y² + 5x − 3y + 4 = 0. Then which of the following statements is (are) TRUE?