Consider the triangle $\Delta ABC$, which $D$ is the midpoint of segment $BC$, and let the point G be defined such that $(GD)= \frac{1}{3}(AD)$. Assuming that $z_A, z_B, z_C$ are the complex numbers representing the points $(A, B, C)$:
a. Find the complex number $z_G$ that represents the point $G$
b. Show that $(CG)= \frac{2}{3}(CF)$ and that $F$ is the midpoint of the segment $(AB)$
How would you go about solving this? I would apply the distance formula but I am not given any actual complex number. I know that a complex number can be represented as a vector connected to origin.