I have added Phantom on my Ark wallet, but do you know how can i backup the private key of this new address ?
The Phantom wallet is using the same private key as your ARK wallet, so you don't have to backup anything.
How did you add the Phantom coins in the first place? Didn't you use the ARK's private key? Well, that's the one you need to keep safe!
good, many thanks
so if i import the ark private key the Phantom address will remain the same ?
Nope, the public address will be different
I'll put their statement as-is in a quote,
We are using ARK public keys that are associated with your ARK public address to generate a PHANTOM based address which will receive the forked credit.
Source:
https://phantom.org/2018/08/28/phantom-zinc-claim-guide%e2%80%8a-%e2%80%8aark/In the images from the guide I linked above, it's obvious that the address has changed. In the first image you can see an ARK address starting with "A" and in the last image an address starting with "P". So the Phantom addresses will be starting with "P". Only the pass-phrase (aka private key) stays the same.
Btw if you use a Ledger Nano, don't put any key you have from your hardware Ledger there, just add the network settings for Phantom and then insert your Ledger (and maybe restart the wallet)