Picturing different functions in the complex plane Just wanted to ask a quick question. Which is, if I am taking a complex function for example: $z = 2x + iy$ then say I wanted to plot it for $x \in (-\infty,\infty)$ where x is a real variable, and $y=0$. What I am wondering is what would that look in in the complex plane ? Would it just be a line along the real axis ? I know it wouldn't be a typical thing someone may do. But I am asking this because I had the idea if, using the complex plane as the vertical axis as the imaginary axis, and the horizontal axis as the real axis.  If my intuition is true then could you also extend this to all real functions such that all real functions be just a flat line that lays along the real axis when plotted in the complex plane ? I do apologize if this is completely trivial but I found it interesting in if this is the case how even complicated real functions would be the same/similar as simple real functions when plotted in the complex plane. If anyone has any suggestions for this please let me know as I find this interesting.

edit: added in the fact the x-variable is a real variable.
This function would simplify to $z=2x$ if you set $y=0$, so it would look like a straight line with slope $2$ in the $z$–$x$ plane (or the $Re(z)$–$x$ plane, if you're thinking of $z$ as complex).

If you want more general visual intuitions for what functions from the complex plane to the complex plane look like, I put together some Python code that helped me a lot—let me know what you think!
This function would simplify to $z=2x$ if you set $y=0$, so it would look like a straight line with slope $2$ in the $z$–$x$ plane (or the $Re(z)$–$x$ plane, if you're thinking of $z$ as complex).

If you want more general visual intuitions for what functions from the complex plane to the complex plane look like, I put together some Python code that helped me a lot—let me know what you think!