For any complex number $$w = c + id$$, let $$arg(w) \in (−\pi, \pi]$$, where $$i = \sqrt{-1}$$ . Let $$\alpha$$ and $$\beta$$ be real numbers such that for all complex numbers $$z = x + iy$$ satisfying $$arg \left(\frac{z + \alpha}{z + \beta}\right) = \frac{\pi}{4}$$, the ordered pair (𝑥,𝑦) lies on the circle
$$x^2 + y^2 + 5x − 3y + 4 = 0$$
Then which of the following statements is (are) TRUE ?

A

$$\alpha = -1$$

B

$$\alpha \beta = 4$$

C

$$\alpha \beta = -4$$

D

$$\beta = 4$$