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What is (a-b)(b-c)(c-a), assuming a, b and c are non-zero complex numbers with the same absolute value and a/b+b/c+c/a is a real number?
You’re gonna need more conditions than that cause you could just slap any a = b = c ∈ ℝ, drop a 0, and call it a day.
The original question was to prove it was equal to 0