Been musing about antonyms and why the difference between the prefix “un” and “im.”
As why “possible” and “impossible”, and “balanced” and “unbalanced,” for example.
Is there any rule regarding this?
How did such prefixes come about? Latin roots, or what?
When you’re through with those words, try “flammable” and “inflammable” Or “valuable” and “invaluable.”
Shot in the dark here but the examples with “im/in” seem to have not only come from Latin (well really medieval French) but were actually made in Latin. What I mean is that maybe examples where we use “un” are for words that we didn’t inherit from Latin or did so more recently, whereas examples with “in”, such as “possible” vs. “impossible” were already present in Latin when it bequeathed them to it’s daughter languages.
Mostly though, there’s not much rhyme or reason to it.
(note: I’m taking “im-” and “in-” to be the same underlying suffix which is changed based on the phonological environment in the surface word).
The etymologies vary, depending upon which un- and which in- you’re talking about.
But, for the most part with the examples you’ve given, un- comes from German, in- comes from Latin (sometimes through French).
Also, it’s grammar and usage. 
I know, I know, I type fast without thinking, expecting spell check will pick up the goofs. i realize now it does not seem to work in the thread title. so it goes.
And panache45, I always love those two words.
What started all this was the question was posed by my Japanese wife. Even having lived here for more than 50 years, she still asks why about English. My only response is, “That is jut the way it is.”
Thanks all, for the info.
Apparently, “unpossible” (spelled “vnpossible” since in older days v and u had different rules) is actually a real English word, so using it doesn’t necessarily mean that you fail English.
Because “in-” can be used as an intensifier:
Thus, “invaluable” means “very valuable.” “Inflammable” comes from “inflame,” which uses the more common version of “in-” meaning “to put into a state.”
I always took “invaluable” to refer to something that literally cannot be assigned a value. Even, say, a diamond that’s worth 100 billion dollars in not invaluable, because its value is 100 billion dollars.
But a one-of-a-kind diamond so rare and special that nobody can determine its comparable worth truly is invaluable.
Or “Your friendship is invaluable to me” means “I couldn’t possibly put a price on our friendship.”
That’s more accurate than “very valuable,” but even then in- is still being used as an intensifier. The thing being described is so valuable that it can’t be valued easily on the scales we typically deal with. That’s definitely a different meaning from simply “not valuable.”
Not only that, but “imbalance” is a commonly used noun and “imbalanced” isn’t an unheard of adjective.