Let P={z ∈ C:|z+2-3 i| ≤ 1} and Q={z ∈ C: z(1+i)+z̄(1-i) ≤-8}. Let in P ∩ Q, |z-3+2 i| be maximum and minimum at z_1 and z_2 respectively. If…

Let $\displaystyle P=\{z \in \mathbb{C}:|z+2-3 i| \leq 1\}$ and $\displaystyle Q=\{z \in \mathbb{C}: z(1+i)+\bar{z}(1-i) \leq-8\}$. Let in $\displaystyle P \cap Q$, $\displaystyle |z-3+2 i|$ be maximum and minimum at $\displaystyle z_1$ and $\displaystyle z_2$ respectively. If $\displaystyle \left|z_1\right|^2+2\left|z_2\right|^2=\alpha+\beta \sqrt{2}$, where $\displaystyle \alpha, \beta$ are integers, then $\displaystyle \alpha+\beta$ equals $\displaystyle \_\_\_\_$.