Let $n$ be a positive integer, $\lambda_{i}$ real numbers and $a_{i}$ for $1\leq i \leq n$ pairwise distinct complex numbers. Help me to prove that if $\forall z \in \mathbb{C}$ we have $ \sum(\lambda_{i}|z-a_{i}|)=0 $, then $\lambda_{i}=0$ for $ 1\leq i \leq n$.
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