Question

If a, b, and c are complex numbers such that |a|=|b|=|c|=1, and a+b+c=0, show that |a-b|=|b-c|=|c-a|, and interpret your result geometrically.

Hint: The relations do not change if we rotate the plane, So we can assume that a=1. Then necessarily c = b̅ = (b̅ / |b|²)