For $(x,y) \in D(0,1)$ fixed, we define the complex number $z = x + iy$ and we set for $t$ real:
$$\mathrm{N}(x,y,t) = \frac{1 - |z|^2}{|z - e^{it}|^2} = \frac{1 - (x^2 + y^2)}{(x - \cos t)^2 + (y - \sin t)^2}$$
Let $t \in [0, 2\pi]$ be fixed. Determine two complex numbers $\alpha$ and $\beta$, independent of $t$ and $z$, such that
$$\mathrm{N}(x,y,t) = -1 + \frac{\alpha}{1 - ze^{-it}} + \frac{\beta}{1 - \bar{z}e^{it}}$$