Is there any interpretation on the Hodge star operator being invariant under holomorphic change of coordinates?

Question

In this wikipedia page, the following is said:

The Hodge star has the remarkable property that it is invariant under holomorphic changes of coordinate.

So, I know three interpretation of holomorphic change of coordinates:

1. Conformality being preserved

2. Infinitesimal shape mapped to similar infinitesimal shape (or , inifinitesimal circle centered get sent to a circle)

3. Squares get sent to squares

Now, could I use this interpretation to understand the Hodge star, or, would there be some other way?