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Question

Mathematics Question on limits and derivatives

Let P=zC:z+23i1P = \\{ z \in \mathbb{C} : |z + 2 - 3i| \leq 1 \\} and Q=zC:z(1+i)+z(1i)8Q = \\{ z \in \mathbb{C} : z(1 + i) + \overline{z}(1 - i) \leq -8 \\}.
Let zz in PQP \cap Q have z3+2i|z - 3 + 2i| be maximum and minimum at z1z_1 and z2z_2, respectively.
If z12+2z22=α+β2|z_1|^2 + 2|z_2|^2 = \alpha + \beta \sqrt{2}, where α\alpha and β\beta are integers, then α+β\alpha + \beta equals ____.

Answer

The correct answer is