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Thanks sandwich!

Should I keep my EOS in a seperated ETH address (with a small amount of ETH)? Or can I still use this ETH address to buy and sell ETH?

You can store there where ever you would like, but be sure to have that wallet mapped to an EOS public key that you posses the private key for.

sandwich, thank you very much!
I bought mine at the exchange kraken.
Do I still have to claim the tokens or is this only when you buy from an ICO?

get ready for 20 complicated steps that, if you dont do perfectly, wil result in you loosing all your EOS! congratulations on doing the work of the EOS team because of their lack of competence! they COULD have figured out a simple way to just redeem all EOS tokens forever period, so people dont end up with illegal expiring digital money that is seriously illegal, (u cnt sell gitf cards or digital money that "expires" theres laws against that"
so Dan and EOS team BETTER fucking promise to BUY UP ALL the unregistered EOS for the actual market price or i smell a lawsuit.