What exactly is the difference between 羡慕, 嫉妒 and 佩服
I know they are all in the realm of admiration/envy/jealousy, but when do I use which?

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Answer

羡慕 = envious (positive)
嫉妒 = jealousy (negative)
佩服 = respectful admiration, like someone bested you in a fair and square way and they earned your respect.

Answer

He doen very good and you hope like too.use 羡慕
He doen very good and you not hope he's  good .use 嫉妒
He doen very good and you very happy for him but not done too. use 佩服

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羡慕。positive。例句：他有很好的天赋，我很羡慕。
嫉妒。negative，=羡慕+觉得不应该这样+希望坏事发生在被嫉妒的人身上。
佩服。positive。例句：他虽然没有很好的天赋，但他通过自己的努力取得成功，我很佩服他。

Answer

羡慕 is similar with envy 嫉妒 as jealousy 钦佩 more like admiration with respect