1.
Let a complex number zz, ∣z∣≠1|z| \neq 1, satisfy log⁡1/2(∣z∣+11(∣z∣−1)2)≤2\log_{1/\sqrt{2}}\left(\dfrac{|z| + 11}{(|z| - 1)^2}\right) \leq 2. Then, the largest value of ∣z∣|z| is equal to: