Are Products of Dirac Delta Functions Well-Defined?

[Muthumanimaran]

Homework Statement

δ(z*-z0*)δ(z+z0)=?
δ(z*+z0*)δ(z-z0)=?

where 'z' is a complex variable 'z0' is a complex number
Formula is just enough, derivation is not needed.

 

[andrewkirk]

The Dirac delta is a distribution, not a number or a function from one number field to another.
The product of distributions is not in general well defined, see here. You can multiply a distribution by a smooth function, but not in general by another distribution.
So the expressions above do not have a clear meaning. They are not well-defined.