So in wolfram alpha it says that $\lim\limits_{x \to 0} \frac{x}{0} = \infty^\sim$ where $\infty^\sim$ symbol is complex infinity.
I find it hard to understand this symbol and the concept, can someone please explain why this happens and why it is undefined.
This happens because we do not know how dividing by 0 looks like and it is simply not defined. You may argue $\lim_{x \rightarrow 0} \frac{x}{x}$ is the same form as you stated. But that is untrue because in your case, we have the fraction a type of $\frac{\rightarrow 0}{exact \;0}$ which is as good as dividing 2 by 0, because in the end $\rightarrow 0$ is still a finite number, just infinitesimally small. And as you do not know what the result of dividing by 0 is, we cannot predict what exactly the outcome may be, imaginary, real or complex