Question 55
Let $a$, $b$, and $c$ be complex numbers such that $|a|=|b|=|c|=1$. If
$$
\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=1
$$
as well, determine the product of all possible values of $|a+b+c|$.
$$
\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=1
$$
as well, determine the product of all possible values of $|a+b+c|$.