Complex Multiplication!

Algebra Level 5

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


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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