「お休みなさい」と「お休みなさいませ」は意味が同じですか。
The other day,I was chatting with someone on Skype,when I suddenly felt sleepy.So I said "Oh,sorry,I feel very sleepy,maybe it is because I've drunk too much at lunch.And that was the reply I then received.

Question

Answer

Both would be used same situation; as you said "I'm sleepy" above.

Then a  friend , a husband or your colleague says to you お休みなさい。

However you as a good old japanese wife, a servant girl, a Hotel stuff or someone ranked lower than adressee in Japanese culture might say お休みなさいませ　to an addressee.

Evden çıkmadan dil öğrenme fırsatını kaçırmayın. Deneyimli dil eğitmenlerimizden oluşan seçkimize göz atın ve ilk dersinize şimdi kaydolun!