Complex Equilateral triangle
Geometry
Level
3
Let there be an equilateral triangle on the complex plane with vertices \(z_1,z_2,\) and \(z_3\). Let the circumcenter of the triangle be \(z_0\).
If \(z_0\ne 0\), find the value of
\[ \frac{(z_1)^2+(z_2)^2+(z_3)^2}{(z_0)^2}. \]
by
avn bha