What is the product of two Dirac delta functions

[Muthumanimaran]

Homework Statement

What is the product of two Dirac delta functions

δ(Real(z-c))δ(Img(z-c))=?
'z' and 'c' are complex numbers.

This is not a problem, But I just need to use this formula in a derivation that I am currently doing. I just want the product of these two Dirac delta functions as a single/double Dirac delta function. I don't need the derivation, just the formula is enough.

 

[mfb]

If your δ are real-valued delta distributions, that product is simply the complex-valued delta distribution, δ(z-c). You can verify this by integrating over the complex plane.