Learn Hardcore German: Nach dem langen Tag bin ich erledigt.

The noun Tag is masculine.
The preposition nach always takes the dative case (when it means after in time).
The definite article for masculine dative singular is dem.

Definite article forms for masculine Tag:

Nominative: der Tag
Accusative: den Tag
Dative: dem Tag ⟵ used here after nach
Genitive: des Tages

So you must say nach dem Tag, not nach den Tag or nach der Tag.

Why is it langen and not langer in nach dem langen Tag?

Because of adjective endings after a definite article in the dative singular masculine.

Pattern with definite article + adjective + noun, masculine dative singular:

dem langen Tag

Explanation:

Tag is masculine.
nach → dative → article dem.
After a definite article in the dative singular, the adjective takes -en:
- dem alten Mann, mit dem neuen Auto, bei dem netten Lehrer.

So you get dem langen Tag, not dem langer Tag or dem lange Tag.

What case does nach take, and what does it mean here?

Case:
The preposition nach takes the dative case when it has a time or abstract meaning like after:

nach dem Essen – after the meal
nach der Arbeit – after work
nach dem langen Tag – after the long day

Meaning here:
In this sentence nach means “after (in time)”. It tells you that the speaker feels erledigt after the long day has finished.

(For comparison: nach Berlin fahren uses nach with place names to mean to Berlin, but that’s a different usage.)

Can I also say Ich bin nach dem langen Tag erledigt? Is there any difference?

Yes, Ich bin nach dem langen Tag erledigt is also correct.

Word order and emphasis:

Nach dem langen Tag bin ich erledigt.
- The time phrase Nach dem langen Tag is put at the beginning for emphasis.
- The finite verb (bin) must stay in second position in a main clause, so the subject ich comes after it.
- Emphasis: After that long day is what you highlight.
Ich bin nach dem langen Tag erledigt.
- This is a more neutral word order.
- The subject ich comes first; the time phrase sits later in the sentence.

Both follow the verb‑second rule and are grammatically fine. The difference is mostly stylistic emphasis, not meaning.

Does erledigt here just mean müde (“tired”), or is it stronger?

Erledigt is usually stronger than simply müde.

Ich bin müde. – I’m tired. (neutral, could be mild)
Ich bin erledigt. – I’m done in / wiped out / completely exhausted.

Nuance of erledigt in this sentence:

Often implies you’re physically or mentally drained from work, stress, or effort.
Sounds like you have no energy left.
Common in spoken German.

Rough English parallels: I’m wiped out, I’m beat, I’m done (in the sense of exhausted).

Is erledigt here an adjective or a verb form?

Formally, erledigt is the past participle of the verb erledigen, but in this sentence it behaves like an adjective.

Verb: erledigen – to take care of / to finish (a task)
- Ich erledige die Arbeit. – I take care of / finish the work.
- Ich habe die Arbeit erledigt. – I have finished the work.
  (erledigt = participle, part of the verb phrase)
Adjectival use with sein:
- Ich bin erledigt. – I am exhausted / done in.
  Here sein is a linking verb, and erledigt is a state you are in, like an adjective (krank, müde, glücklich).

So grammatically: bin (form of sein) + erledigt (predicative adjective derived from a participle).

Can erledigt also mean “finished” instead of “exhausted”?

Yes, erledigt can mean “finished / completed”, but that depends on what the subject is.

Thing as subject → “finished / completed”
- Die Arbeit ist erledigt. – The work is done / finished.
- Die Aufgabe ist erledigt. – The task is completed.
Person as subject → “exhausted / done for”
- Ich bin erledigt. – I’m exhausted (or, in some contexts, “I’m done for / I’m in big trouble”).
- In your sentence it clearly means physically/mentally exhausted after the long day.

So:

Person + sein + erledigt → usually exhausted / done for.
Thing + sein + erledigt → finished / completed.

Is erledigt in this sense formal, informal, or slangy?

Ich bin erledigt is:

Natural in everyday spoken German.
Acceptable in informal writing (messages, emails to friends).
Fine in neutral contexts; it’s not vulgar or very slangy.
Slightly less formal than Ich bin sehr müde, but still not crude.

In a very formal written context (e.g. a business report), you’d more likely use something like:

Ich bin sehr erschöpft.
Der Tag war sehr anstrengend.

But in conversation, Ich bin erledigt is very common and idiomatic.

Do I need a comma after Nach dem langen Tag?

No, you do not need (or want) a comma there in this simple sentence:

Nach dem langen Tag bin ich erledigt. ✅

There is only one main clause, and Nach dem langen Tag is just a prepositional phrase (a time adverbial). German does not put a comma between a fronted prepositional phrase and the rest of a simple main clause.

You would use a comma if there were an additional clause, for example:

Nach dem langen Tag, den wir hatten, bin ich erledigt.
(Here den wir hatten is a relative clause, so commas are required.)

How would this sentence change with other genders or with plural nouns?

The structure stays the same: nach + dative article + adjective (‑en) + noun.

Some examples:

Feminine:
- Nach der langen Nacht bin ich erledigt.
  (night = die Nacht, dative singular feminine → der, adjective → langen)
Neuter:
- Nach dem langen Meeting bin ich erledigt.
  (meeting = das Meeting, dative singular neuter → dem, adjective → langen)
Plural:
- Nach den langen Tagen bin ich erledigt.
  (days = die Tage, dative plural → den, adjective → langen; note -n on Tagen in dative plural)

So the pattern nach + dative + langen + [time word] stays, and only the article and noun form change with gender/number.