Argument of Dirac delta function is quadratic with complex roots

1. Is Dirac delta function complex?
2. What are the properties of Dirac delta function?
3. How do you prove properties of Dirac delta function?

Is Dirac delta function complex?

1(a). Here we consider a generalization, ˜δ(z), of the Dirac delta function (also a distribution) whose argument is allowed to be a complex variable.

What are the properties of Dirac delta function?

In mathematics, the Dirac delta distribution (δ distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one.

How do you prove properties of Dirac delta function?

Over this very small range of x, the function f(x) can be thought to be constant and can be taken out of the integral. From the definition of the Dirac delta function, the integral on the right-hand side will equal 1, thus proving the theorem.