\text{In one of the questions above, you proved that} \,\, z_{1}^{2}+z_{2}^{2}+z_{3}^{2}=z_{1}z_{2}+z_{1}z_{3}+z_{2}z_{3} \,\, \text{where the points} \,\, z_{1}, z_{2} \,\, \text{and} \,\, z_{3} \,\, \text{were the vertices of an equilateral triangle.} \\\\ \therefore...