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On the store page, it says "Baldur's Gate II: Enhanced Edition includes the classic Baldur's Gate 2 Complete." so, where do I download the complete edition?
This question / problem has been solved by advowsonimage
The store page is wrong. Buying EE gets you a GOG gift code that can be redeemed for the Classic Edition. Once redeemed, you will have Classic Edition in your account as a separate product. To see your gift code, open the Enhanced Edition in your account's games listing, choose More -> Serial Keys. Note that GOG sometimes runs out of keys, in which case you will need to remind Support to get more serial keys.
Thanks for the heads-up!