# Kreisscheibe/C/n Punkte/Gibt Punkt mit Abstand mindestens n/Aufgabe/en

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

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