在 + adjective/verb gives the progressive 'be -ing'. 忙 ('busy') doubles as a verb here ('to be busy / be occupied with') — Chinese adjectives often verb up like this. Compare 我在睡觉 ('I'm sleeping').
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Casual; fine with friends and peers. For a boss or stranger, soften with 不好意思 first or use 我现在有点忙.
