Why can finite elements handle complex geometries, but finite differences can't?

Hello all:

I'm new to the world of finite elements/finite differences. I'd like to understand the advantages of the finite element method. I read that the finite difference method cannot handle complex (e.g., curved domains, fractures) geometries. I have had no luck in understanding why. I would appreciate any help! Thanks.

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AlephZero
It is not true that all finite element formulations can handle complex geometries well. For example some high-order elements have "weird" nodal variables (for example derivatives like $\partial^3 F / \partial^2 u \partial v$ where u and v are the directions along the edges of the element) which don't match up properly unless adjacent elements have consistent geometry, and/or the corresponding boundary conditions too hard to specify for arbitary shapes.