Showing the limit does not exist

Question

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?

Answer 1

hint:Take two different path to $0$: $z = x+ix$, and $z = x+ i2x$, and take limit as $x \to 0$.