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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 

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

 

 

 

 

I know I asked this question before, but there was no response so I thought I would try again.  I honestly do not know the answer, anyone with complex number experience, help would be greatly appreciated.  

 Jun 5, 2021
 #1
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By the Triangle Inequality, the maximum value is 2^6 = 64.

 Jun 6, 2021

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