Learn Hardcore Swedish: Jag tänker inte köpa en dyr jacka. - I am not planning to buy an expensive jacket.

tycker att (opinion): Jag tycker att det är dyrt.
tror att (belief/guess): Jag tror att det blir regn.
For “think about/of,” use tänker på: Jag tänker på dig.

Why is there no att before köpa?

After modal/semi-modal verbs that express ability, desire, obligation, habit, or intention, Swedish normally drops att: ska, vill, kan, måste, bör, får, brukar, hinner, and also tänker when it means “intend.” Hence: Jag tänker köpa …, not Jag tänker att köpa ….
Note: tänker att can appear before a full clause (some speakers use it like “I think that”), but not before an infinitive: ✔ Jag tänker att vi …, ✘ Jag tänker att köpa ….

Where does inte go, and can I say “Jag tänker köpa inte …”?

Put inte after the finite verb in main clauses. Here the finite verb is tänker, so: Jag tänker inte köpa ….
✘ Jag tänker köpa inte … is unidiomatic.
With only one verb: Jag köper inte en dyr jacka. Same rule: finite verb + inte.

Could I use ska or kommer att instead of tänker?

Jag ska inte köpa … = I’m not going to (plan/arrangement/decision).
Jag kommer inte att köpa … = I won’t buy (prediction/expectation).
Jag tänker inte köpa … = I don’t intend to (current intention).
All are grammatical; nuance differs.

Why en dyr jacka (not “ett” or a different adjective form)?

Jacka is an “en-word” (common gender), so the indefinite singular is en jacka, and the adjective is base form dyr: en dyr jacka.

Ett-word: ett dyrt hus
Plural/definite: dyra (see below).

When would I say den dyra jackan instead?

Use the definite form when a specific, known jacket is meant: den dyra jackan (“the expensive jacket”).
Pattern (double definiteness): den/det/de + adj in -a + noun in definite
Examples: den dyra jackan, det dyra huset, de dyra jackorna.

Should I use ingen/inget/inga instead of inte here?

Both are possible but they negate different things:

Jag tänker inte köpa en dyr jacka. = I’m not going to buy an expensive jacket (often implies I might buy a cheaper one).
Jag tänker inte köpa någon dyr jacka. = I’m not going to buy any expensive jacket at all (stronger).
With no auxiliary: Jag köper ingen dyr jacka. (general statement: I don’t buy expensive jackets.)

Can I drop the article and say Jag tänker inte köpa dyr jacka?

No. Singular count nouns normally need an article in Swedish. Say en dyr jacka.
Article-less is fine with mass nouns: köpa kaffe, or in headlines/telegraphese.

How do I pronounce the sentence?

A careful pronunciation: [jɑːɡ ˈtɛŋkɛr ˈɪntɛ ˈɕøːpa en dyːr ˈjakːa]
Tips:

ä in tänker ≈ [ɛ] (like “bed”).
k before ö in köpa is the soft “kj”-sound [ɕ].
ö in köpa ≈ rounded mid-front vowel [øː].
y in dyr is a long front rounded vowel [yː] (shape lips like “oo” but say “ee”).
j in jacka is like English “y”; ck is a long [kː].
Many speakers assimilate r + n: tänker inte can sound like [tɛŋkɛ ɳɪntɛ]. This varies by region.

What happens if I start with an adverb like “tomorrow”?

Swedish main clauses are V2: the finite verb stays in second position.
Example: Imorgon tänker jag inte köpa en dyr jacka.
(Fronted adverbial → finite verb → subject → inte …)

How do I talk about past intention or a completed action?

Past intention: Jag tänkte inte köpa en dyr jacka. = I wasn’t going to / didn’t intend to.
Completed action: Jag köpte inte en dyr jacka. (Often better as Jag köpte ingen dyr jacka to avoid ambiguity.)

Is tänker a modal verb?

Not traditionally, but here it behaves like a semi-modal that governs a bare infinitive and expresses intention. For firm arrangements, ska is common; for predictions, kommer att.

Can I put inte at the very end, like “Jag tänker köpa en dyr jacka inte”?

No. That’s not normal Swedish word order. Keep inte after the finite verb: Jag tänker inte köpa …

Do I have to keep the subject Jag, or can I drop it?

Keep it. Swedish is not a pro-drop language in standard usage: Jag tänker …
Dropping the subject occurs only in very informal ellipsis (notes, headlines, texting).

Is ej a possible replacement for inte?

Grammatically yes, but ej is formal/old-fashioned and common on signs: Ej öppet. In everyday speech/write inte: Jag tänker inte …

What’s the difference between jacka, kappa, and rock?

jacka = jacket (short, casual or outdoor).
kappa = long coat, traditionally for women.
rock = long coat, traditionally for men.
So your sentence specifically says “jacket,” not “coat.”

Where do pronoun objects go relative to inte?

Pronoun objects move before inte: Jag tänker inte köpa den.
Full noun phrases usually stay after inte: Jag tänker inte köpa en dyr jacka.