Jeg gemmer nøglen i min lomme.

Because nøglen is the definite form: the key.

In Danish, many nouns add a suffix for definiteness:

• en nøgle = a key
• nøglen = the key

So Jeg gemmer nøglen i min lomme uses the key, not a key.

The -n is the definite ending for a common-gender noun.

For this noun:

• en nøgle = a key
• nøglen = the key

This is very common in Danish. Instead of putting a separate word before the noun, Danish often attaches definiteness to the end of the noun.

Because Danish normally does not use the definite ending when there is already a possessive word like min, din, hans, vores, etc.

So:

• min lomme = my pocket
• not min lommen

Compare:

• lommen = the pocket
• min lomme = my pocket

A possessive already makes the noun specific, so the extra definite ending is not used.

Because lomme is a common-gender noun, and common-gender nouns take min.

Danish possessives agree with the noun:

• min for common gender
• mit for neuter
• mine for plural

So:

• en lomme → min lomme
• if it were a neuter noun (et-word), you would use mit

Gemmer is the present tense of gemme.

• at gemme = to keep / store / hide / save
• jeg gemmer = I keep / I am keeping / I hide / I am hiding, depending on context

Danish present tense is often formed by adding -r to the infinitive:

• gemme → gemmer

Because gemme is the infinitive form, while gemmer is the form used with jeg in a normal present-tense sentence.

Compare:

• at gemme = to keep / to hide
• jeg gemmer = I keep / I hide

So in a full statement, Danish needs the finite verb form gemmer.

No. Gemme can have several related meanings, such as:

• hide
• keep
• store
• save

The exact translation depends on context.

In Jeg gemmer nøglen i min lomme, it could mean something like:

• I keep the key in my pocket
• I hide the key in my pocket

If the meaning has already been given to the learner, it is still useful to know that gemme is broader than just one English verb.

This is the normal Danish word order for a simple statement:

subject + verb + object + adverbial/prepositional phrase

So here:

• Jeg = subject
• gemmer = verb
• nøglen = object
• i min lomme = prepositional phrase

This is very similar to basic English word order:

• I keep the key in my pocket

I usually means in.

So:

• i min lomme = in my pocket

That is the natural preposition here because the key is located inside the pocket.

In modern spoken Danish, jeg is often pronounced roughly like yai or yaiy, depending on accent and speaking style.

A few important points for an English speaker:

• the j sounds like English y
• the written g is not pronounced like a hard English g
• the whole word is often smoother and less sharply pronounced than the spelling suggests

So do not pronounce it like jegg.

The hardest part for many English speakers is ø.

A rough guide:

• nø- has a front rounded vowel that English does not really have
• -glen is not pronounced with a strong English g
• the ending -en is usually a light, unstressed ending

A rough learner-friendly approximation might be something like NUH-len or NER-len, but neither is exact. The important thing is that ø is its own Danish vowel and needs practice.

It is an en word:

• en lomme = a pocket

That matters because it affects things like:

• the indefinite article: en
• the possessive: min lomme
• the definite form: lommen

So learning the gender together with the noun is very helpful:

• en lomme
• en nøgle

Yes, depending on context.

Danish present tense often covers both:

• simple present: I keep
• present progressive: I am keeping

So jeg gemmer does not by itself force one English tense choice. The surrounding context decides which English translation sounds best.