Are some functions restricted to real or imaginary numbers?

I mean, if you can verify/validate a formula over the real values... how do we verify that it still works over the imaginary and complex values when our normal means of conceptualizing no longer apply.





I have found formulas in math that make perfect sense in real values. But new formulas are derived from their application to imaginary values... which, even though I can work the math, I dont conceptualize the formula - I dont see that it should work.Are some functions restricted to real or imaginary numbers?
Can you do integral approximations with imaginary numbers, or is that a null concept ?





Been a while since I did any real math. Just do a little for fun, these days.





This might help. I've not read it through though - http://people.hofstra.edu/Stefan_Waner/r鈥?/a>Are some functions restricted to real or imaginary numbers?
can you provide an example?





I think, maybe, some math is taken for granted... as a rule... and isnt really respected. That mathematicians have naively and arrogantly taken it for what its worth just because it follows with a little logic... but with no regard for realistic or practical meaning.





I heard that sometimes. I think some part of math has a lot to do with practical things. Even complex numbers used for applications in engineering or other domains.


On the other hand a good part doesn't have immediate utility.


They are just for the sake of it and the results are a material that may be used in future or...not.