Find $\displaystyle \displaystyle\lim_{z \to 0} \frac{\bar{z}^2}{z}$

Attempt: I thought that this limit might not exist since if you let $\displaystyle z = x + iy$, then when approaching from y-axis, the limit equals $\displaystyle iy$ and when approaching from the x-axis, the limit equals $\displaystyle x$.

However the solution says that limit is actually 0. I'm not sure how to get this result.

Any suggestions?