How to find the maximum possible value of $\big| (z_1-z_2)^2+(1-z_1)(1-z_2) \big|$ given that $|z_1|=|z_2|=1$?
How to find the maximum and minimum value of $\left|(z_1-z_2)^2 + (z_2-z_3)^2 + (z_3-z_1)^2\right|$ (where $|z_1|=|z_2|=|z_3|=1$)?