I am trying to show $\lim_{z \to 0} f(z)$ does not exist where $f(z)=\frac{xy}{2x^2+3y^2} +ix^2$.
I am to show the limit does not exist by taking the limit along the straight line $y=mx$ where m is a constant.
My plan is to show that the limit depends on the path taken. Do I do this by first considering $y=2x$ then $y=3x$ and showing they give different answers?