새해 복 많이 받으세요. (sae-hae bok ma-ni ba-deu-se-yo)
행복한 새해 되세요. (haeng-bo-kan sae-hae dwe-se-yo)
A breakdown of the phrases:
새해 (sae-hae): new year
복 (bok): good fortune
많이 (ma-ni): a lot, many
받으세요 (ba-deu-se-yo): receive please
Literal translation: Please receive a lot of good fortune in the new year.
행복한 (haeng-bo-kan): happy
새해 (sae-hae): new year
되세요 (dwe-se-yo): become please
Literal translation: Please become a happy new year.
Or just: Happy new year!
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