Simplify question regarding Simplify[Im[1/a], {Element[a, Reals]}]

Questions
1

I’m sure this has a simple explanation. Can someone help me understand why the following does not simplify to 0?

In: Simplify[Im[1/a], {Element[a, Reals]}]

Out: Im[1/a]

Thanks in advance!

2

Probably because of the singularity at 0:

Simplify[Im[1/a], {a > 0 || a < 0}]

gives 0