Consider the holomorphic curve $$ \Gamma:=\left\{(z, w) \in \mathbb{C}^{2}: z^{2}=w^{3}\right\} $$
My question is how can I imagine this? I studied that a holomorphic curve in $\mathbb{C}^n$ is a holomorphic map from an open set of the complex number to $\mathbb{C}^{n}$ for some $n$. If it were a real curve I would have no difficulties in parametrizing it with a parameter $t$ and seeing that the form it takes is the curve $y=x^{\frac{2}{3}}$, which is a cusp with a singularity in the origin. My question is how can I imagine the following curve in the complex numbers? How can I prove it has a singularity in the origin? Thanks!