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Let \(a, b, c, d\) be distinct complex numbers such that \(|a| = |b| = |c| = |d| = 1\) and \(a + b + c + d = 0\). Find the maximum value of 

\(|(a + b)(a + c)(a + d)(b + c)(b + d)(c + d)|\).

 Oct 11, 2020
 #1
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By the triangle inequality, |a + b| <= |a| + |b| = 2, so the whole product has a maximum of 2^6 = 64.

 Oct 11, 2020
 #2
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This doesn't seem to be correct.

WarpPrime  Oct 12, 2020

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