It is known (and can be easily shown) that if complex numbers $a, b, c$ form an equilateral triangle on the complex plane, then $$a^2+b^2+c^2=ab+bc+ca$$
Question Is there a geometric significance/interpretation of
- the squares of each of these numbers, as well their sum (i.e. LHS), and
- the product of pairs of each of the numbers, as well as their sum (i.e. RHS)?