P, Q represent complex numbers $\displaystyle \alpha ,\beta $ respectively where O is the origin and O, P, Q are not collinear. In triangle OPQ, the median from O to the midpoint M of PQ meets the median from Q to the midpoint N of OP in the point R, where R represents the complex number z.

Show that $\displaystyle z=\frac{1}{3}(\alpha +\beta )$ and deduce that R is the point of concurrence of the three medians of triangle OPQ