
unmöglich
impossible
Describes something that cannot happen, exist, or be done; not feasible.
Es ist unmöglich, ohne Sauerstoff zu atmen.
It is impossible to breathe without oxygen.
impossible
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impossible
Describes something that cannot happen, exist, or be done; not feasible.
Es ist unmöglich, ohne Sauerstoff zu atmen.
It is impossible to breathe without oxygen.

unacceptable
Describes behavior or a person as completely unacceptable, rude, or unbearable.
Sein Benehmen bei der Feier war wirklich unmöglich.
His behavior at the party was really unacceptable.

extremely
A colloquial, often ironic intensifier meaning 'extremely' or 'incredibly'. It can be used both positively and negatively.
Sie sieht in diesem Kleid unmöglich gut aus.
She looks impossibly good in this dress.
The word is the direct opposite of 'möglich' (possible). The prefix 'un-' is often used in German to negate the meaning of adjectives.
Ohne das richtige Werkzeug ist die Reparatur unmöglich.
Without the right tool, the repair is impossible.
In the meaning of 'not feasible', 'unmöglich' (impossible) is very often used in the structure 'es ist unmöglich, etwas zu tun' (it is impossible to do something). This is followed by an infinitive clause with 'zu'.
Es ist unmöglich, diese Aufgabe in nur einer Stunde zu erledigen.
It is impossible to complete this task in just one hour.
If you want to describe behavior as unacceptable, you can say 'jemand benimmt sich unmöglich' (someone behaves unacceptably) or 'jemandes Verhalten ist unmöglich' (someone's behavior is unacceptable). This use expresses strong criticism.
Er hat sich auf der Feier allen Gästen gegenüber unmöglich benommen.
He behaved unacceptably toward all the guests at the party.
The use as an intensifier meaning 'extremely' is purely colloquial. In this function, 'unmöglich' (impossibly/extremely) stands directly before the adjective it intensifies.
Die Party gestern war unmöglich lustig.
The party yesterday was impossibly funny.
incredible
As colloquial intensifiers, both words can express an extreme degree. „Unglaublich“ usually emphasizes astonishment, while „unmöglich“ can additionally suggest excess or disapproval. Use „unglaublich“ for surprised admiration and „unmöglich“ when the extreme degree seems more problematic.

Der Kaffee war unmöglich heiß, sodass ich ihn sofort wegstellen musste.
The coffee was impossibly hot, so I had to put it down immediately.
Der Kaffee war unglaublich heiß, aber nach kurzer Zeit konnte ich ihn trinken.
The coffee was incredibly hot, but I could drink it after a short while.