Learn Croatian: Ja ću rješavati zadatak, a ti ćeš se odmarati. - I will be solving the task, and you will be resting.

Both rješavati (to be solving) and odmarati se (to be resting) are imperfective verbs. We use them here because we want to focus on these actions as continuous processes taking up time in the future, rather than as completed events. You can see this reflected in the English translation: "will be solving" instead of "will solve".

Usually we drop subject pronouns like ja and ti in Croatian. Why are they used in this sentence?

You are right that subject pronouns are usually dropped because the verb forms (ću and ćeš) already tell us who is doing the action. However, they are kept here to create a strong contrast. By explicitly saying ja... a ti..., the speaker is heavily emphasizing the difference between what I will be doing and what you will be doing.

Why does the sentence use a for "and" instead of the usual i?

In Croatian, a is a contrasting conjunction. It can translate to "and" or "but", and it specifically shows a shift in focus or a mild contrast (much like "whereas" or "while" in English). Since my hard work is being contrasted with your resting, a is the natural choice instead of i, which just groups similar things together.

In the second half of the sentence, why are ćeš and se placed exactly where they are?