Yeah "computable" may not be the best word to describe the sort of numbers that i seems to constitute an exit from, but then again I wouldn't say "real" makes much sense either. I guess I just mean conceivable, at least for me. I cannot conceive of the square root of -1, but you're right that doesn't mean I cannot compute it via i as a sort of proxy.I dunno.
Don't get too hung up on this I think. They were invented to get past an impasse but as soon as they were out of the box then they took on a life of their own. They are as computable as anything else now, probably best seen as one of a list of types of numbers that were called into existence as they were needed (see post above).