I have to evaluate the following limit:
$$\lim_{z\rightarrow \frac{\sqrt3i}{2}}\frac{z}{4z^2+3}$$
I know the limit doesn't exist. I tried proving it by letting: $$z = x +iy,\\y =\frac{\sqrt3i}{2} $$
And then evaluating the new limit for $$x\rightarrow0\_$$
and $$x\rightarrow0_+$$
and hence show they do not equal one another. However, this approach didn't work since I got to $$\lim_{x\rightarrow0\_}\frac{x+i\sqrt3/2}{4x(x+i\sqrt3)}$$
and got stuck.
Could I get some help guys?
Edit: sorry if the formatting isn't that good. I'm still new to this site.