Is this another way of saying how are you? or are they really asking if you slept well? because I understand Korean usually has multiple meanings for some words and phrases.
whats up
잘자요 (잘 자요 in correct orthography) means “Good night!”, not “How are you?”.
The lesson has a mixture of different greetings.
“잘”, an adverb meaning “well, happily, with good results, etc” is widely used in greetings and other contexts.
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잘 자(요): 잘 + 자다(sleep) + 요 => “sleep well” => Good night (greeting when going to bed).
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잘 가(요): 잘 + 가다(go) => “go well” => take care (greeting when parting).
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잘 있어(요): 잘 + 있다(stay) => “stay wel” => take care (when leaving someone house).
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잘 지내(요): 잘 + 지내다(pass time, live) => take care (when parting for a longer period).
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잘 있었어? = 잘 지냈어?: Have you been alright? / How have you been? (= 안녕하셨어요?)
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잘 잤어?: Did you have a good sleep? = 안녕히 주무셨어요? (formal and polite)
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잘해 / 잘해 봐: Do your best / good luck!
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잘됐다: That is great / I am happy for that ( <-> 안됐다: that’s too bad ).
Hello there.
Thank you. Gamsahabnida.