好久 (hǎo jiǔ) is a colloquial set phrase meaning 'quite a while, a long time' — it's often used in negative sentences like 好久没... (haven't done something for a long time). Unlike 久 (jiǔ), which is a general adjective for 'long (time)', 好久 emphasizes a noticeable duration; 半天 (bàn tiān) can also mean 'a long time' but literally means 'half a day' and often carries a tone of impatience or exaggeration.