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
\(|(a + b)(a + c)(a + d)(b + c)(b + d)(c + d)|\).
By the triangle inequality, |a + b| <= |a| + |b| = 2, so the whole product has a maximum of 2^6 = 64.
This doesn't seem to be correct.
+19 
