Question 19
Find all triples $(a, b, c)$ of non-zero complex numbers with equal absolute values, for which
$$
\frac{a}{b} + \frac{b}{c} + \frac{c}{a} + 1 = 0.
$$
$$
\frac{a}{b} + \frac{b}{c} + \frac{c}{a} + 1 = 0.
$$
MathNet 2015-part-05 — 191 problems (EN–VI) Question 19
Math Olympiad Vault · MathNet 2015-part-05 — 191 problems (EN–VI)