1.
Let C\mathbb{C} be the set of all complex numbers. Let S1={z∈C:∣z∣≤1}S_1 = \{z \in \mathbb{C} : |z| \le 1\} and S2={z∈C:z(1+i)+zˉ(1−i)≥4}S_2 = \{z \in \mathbb{C} : z(1 + i) + \bar{z}(1 - i) \ge 4\}. Then, the maximum value of ∣z−1z∣\left|z - \dfrac{1}{z}\right| for z∈S1∩S2z \in S_1 \cap S_2 is equal to: