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Found problems: 1

2014 Harvard-MIT Mathematics Tournament, 9
Tags: polynomial , geometry , algebra , function , hmmt , complex number , fermat point
Given $a$, $b$, and $c$ are complex numbers satisfying \[ a^2+ab+b^2=1+i \] \[ b^2+bc+c^2=-2 \] \[ c^2+ca+a^2=1, \] compute $(ab+bc+ca)^2$. (Here, $i=\sqrt{-1}$)