MathematicsMedium53×since 2002Q3165Let S=∣z∈C:∣z−1∣=1\mathrm{S}=|\mathrm{z} \in \mathrm{C}:| z-1 \mid=1S=∣z∈C:∣z−1∣=1 and (2−1)(z+zˉ)−i(z−zˉ)=22∣(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2 \sqrt{2} \mid(2−1)(z+zˉ)−i(z−zˉ)=22∣. Let z1,z2∈Sz_1, z_2 \in \mathrm{S}z1,z2∈S be such that ∣z1∣=maxz∈s∣z∣\left|z_1\right|=\max\limits_{z \in s}|z|∣z1∣=z∈smax∣z∣ and ∣z2∣=minz∈S∣z∣\left|z_2\right|=\min\limits _{z \in S}|z|∣z2∣=z∈Smin∣z∣. Then ∣2z1−z2∣2\left|\sqrt{2} z_1-z_2\right|^22z1−z22 equals :A1B4C3D2Check answerSkip