Question 14
Let $a, b, c \in \mathbb{C}^*$ be distinct and have the same modulus, such that
$$
a^{2}+b^{2}+c^{2}+a b+a c+b c=0.
$$
Prove that $a, b, c$ are the affixes of the vertices of a right-angled or equilateral triangle.
$$
a^{2}+b^{2}+c^{2}+a b+a c+b c=0.
$$
Prove that $a, b, c$ are the affixes of the vertices of a right-angled or equilateral triangle.