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Let $\{z_i\}$, $i=1,2,\ldots,n$ be a set of complex numbers. Then I know that there is a set $J$ such that $\left|\sum_{j\in J} z_j\right|\ge \frac{1}{\pi} \sum_{k=1}^n |z_k|. $ However, how do I show that there's some other set, say M such that $\left|\sum_{j\in M} z_j\right|\ge \frac{1}{8} \sum_{k=1}^n |z_k|. $

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    @Srivatsan: I am interested! You should not feel sorry for sharing :-)2012-01-26

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