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 
