Disk/C/N points/Exist point with distance above n/Exercise

Consider ${}n$ complex numbers ${}z_{1},z_{2},\ldots ,z_{n}$ lying in the disc ${}B$ with center ${}(0,0)$ and radius ${}1$, that is in ${}B={\left\{z\in \mathbb {C} \mid \vert {z}\vert \leq 1\right\}}$. Prove that there exists a point ${}w\in B$ such that

${}\sum _{i=1}^{n}\vert {z_{i}-w}\vert \geq n\,.$

Create a solution