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Can anyone help on the following question?

Are there five complex numbers $z_{1}$, $z_{2}$ , $z_{3}$ , $z_{4}$ and $z_{5}$ with $\left|z_{1}\right|+\left|z_{2}\right|+\left|z_{3}\right|+\left|z_{4}\right|+\left|z_{5}\right|=1$ such that the smallest among $\left|z_{1}\right|+\left|z_{2}\right|-\left|z_{1}+z_{2}\right|$, $\left|z_{1}\right|+\left|z_{3}\right|-\left|z_{1}+z_{3}\right|$, $\left|z_{1}\right|+\left|z_{4}\right|-\left|z_{1}+z_{4}\right|$, $\left|z_{1}\right|+\left|z_{5}\right|-\left|z_{1}+z_{5}\right|$, $\left|z_{2}\right|+\left|z_{3}\right|-\left|z_{2}+z_{3}\right|$, $\left|z_{2}\right|+\left|z_{4}\right|-\left|z_{2}+z_{4}\right|$, $\left|z_{2}\right|+\left|z_{5}\right|-\left|z_{2}+z_{5}\right|$, $\left|z_{3}\right|+\left|z_{4}\right|-\left|z_{3}+z_{4}\right|$, $\left|z_{3}\right|+\left|z_{5}\right|-\left|z_{3}+z_{5}\right|$ and $\left|z_{4}\right|+\left|z_{5}\right|-\left|z_{4}+z_{5}\right|$is greater than $8/25$?

Thanks!

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    Are you sure there is no typo in your question?2012-11-13
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    Christian, sorry, the updated question is actually the one I really wanted to ask. Thanks.2012-11-13
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    Why is there no link to the previous question: http://math.stackexchange.com/questions/234481/does-this-hold ... or if you ask this one independently of that other one, the two of you need to talk.2012-11-13
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    For clarity's sake it might be better to write the condition as $\min_{i,j: i\neq j} |z_i|+|z_j|-|z_i+z_j|$...2012-11-13
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    GEdgar, the OP there might have asked a somewhat different question. But this question looks simple and concrete, so a complete answer to this question would be very inetersting.2012-11-14

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