it is only a mere curiosity of calculus and do not if has any application
the idea is how can we define the apparently impossible functions
for m a real number
a can be a real or complex number
a and b are real numbers a,b >0
but 'f' is a complex valued function even for real 'x'
as you can see all of them make no sense for any x real or complex since we always would have the same answer
for every real or complex 'x'