Question: A science policy analyst is modeling energy transmission efficiency across a network of nodes arranged in a regular hexagon. One node is at the origin $O$, and adjacent nodes are at $A = (1, 0)$, $B = \left(\frac12, \frac\sqrt32\right)$, and $C = \left(-\frac12, \frac\sqrt32\right)$. The analyst wants to find the complex number $z$ representing the node opposite to $O$, assuming integer coordinates are used in a scaled grid. Find the coordinates of this farthest node. - Groen Casting