A triangle and its median in complex plane. Let $z_1$, $z_2$, $z_3$ be vertices of the triangle $\triangle ABC$. And given that $|z_1|=|z_2|=|z_3|$. Then the median through $A$ cuts the circumcircle at which point? 
We need to get the answer in terms of the complex numbers $z_1$, $z_2$, $z_3$.
Any hints would be helpful.

Hints:
Note that, since $z_1$,$z_2$, and $z_3$ all have equal magnitude, then they all lie on a common circle centred at the origin. Observe that this circle is the circumcircle of your triangle.
Now just create a line which goes through the point A and the mid-point of the opposite side.
Can you continue from here?
