Complex Multiplication!

Algebra Level 4

aa, bb, cc and dd are non-zero complex numbers that satisfy

a+b+c+d=a3+b3+c3+d3=0a+b+c+d=a^3+b^3+c^3+d^3=0

The sum of all possible values of (a+b)(a+c)(a+d)(a+b)(a+c)(a+d) can be expressed as p+qip+qi where pp and qq are real numbers and ii is the imaginary unit that satisfies i2=1i^2=-1. What is p+qp+q?


This problem is inspired by a problem that appeared in ITT - 19941994.


This problem is from the set "Olympiads and Contests Around the World -1". You can see the rest of the problems here.

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