MathNet 2016-part-04 — 184 problems (EN–VI) Question 31

Let $a$, $b$, $c$ be complex numbers such that $|a-1| = |b-2| = |c+3|$ and $a + b + c = 0$. Show that $|a-b+1| = |a-c-4| = |b-c-5|$.