Can someone explain the intuition behind integral transforms such as Laplace transform. Why do they say LT is a complex function of a complex variable vs FT being a complex function of a real variable??
LT: b+jw
FT: jw

Both look like complex numbers. In case of FT, the variable is w? What about LT, is there two variables, b and w?
So: e^jwt vs e^(b+jw)t
where is the complex and where is the real variable here?
We can expand e^(b+jw)t as e^ bt e^jwt in which case e^bt is a time dependent magnitude. I get that but I am still confused about complex vs real arguments.

What is the relationship with power series? How do I get connect all the dots? I am confused.