I don't know what you mean by "validity". I am absolutely certain that applications of all the "standard" fields (real, complex, algebra) can be found. They aren't bad things to learn.

I'm just suggesting that from what I've seen, the other fields I listed are more commonly useful. Everyone I know, across pure and especially applied math has used probability and linear algebra. Lots of people haven't used complex analysis or algebra ever, except on the qual.