"dich" in "Ich glaube (an) dich" — accusative or dative?

Question

Is the "dir" in "Ich glaube an dich." in accusative case while "dich" in "Ich glaube dich." in dative case, not the other way?

I encounter this in Duolingo and it seems very quirky and counter-intuitive.

Answer 1

"Glauben" can take both a dative and an accusative object. The person you believe must be in the dative, and what you believe in the accusative. Example:

Ich glaube dir deine Erklärung.

The accusative object is often a subordinary clause (Objektsatz). Example:

Ich glaube dir, dass das keine Absicht war.

With the preposition "an" things are different. In that case, you must use the accusative after "an".

Answer 2

In German language, you should not only learn the verb but also its details like whether it is seperable or not, takes dative or accusative, accepts a preposition or not, must take an object or not necessarily and so on.

In your question, glauben takes dative and because of this reason, it should be;

Ich glaube dir

or if you want to emphasize "believing with taste of the trust", the verb glauben takes preposition an and in such a case, you can also say;

ich glaube an dich

And you can also ask why did preposition an take an accusative instead of dative. It would require a huge explanation but briefly, I can say some prepositions take accusative, some prepositions take dative and some prepositions are two-way prepositions, meaning they can take either accusative or dative based on the situation. The preposition an, which glauben takes, is also one of the two-way prepositions and in case of glauben, it takes accusative instead of dative, resulting ich glaube an dich instead of ich glaube an dir.

Answer 3

Well, if it's dich, it can only be in the accusative case. And dir can only be in the dative case. These are fixed pronominal forms.