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i doesn't belong to QQbar ? Why ?

I do not understand this :

sage: sqrt(1) in QQbar
True
sage: sqrt(-2) in QQbar
True
sage: sqrt(-1) in QQbar
False

Can someone explain ?

i doesn't belong to QQbar ? Why ?

I do not understand this :

sage: sqrt(1) in QQbar
True
sage: sqrt(-2) in QQbar
True
sage: sqrt(-1) in QQbar
False

Can someone explain ?

Note that, however :

sage: [t[0] in QQbar for t in (x^2+1).roots(ring=QQbar)]
[True, True]

i doesn't belong to QQbar ? Why ?

I do not understand this :

sage: sqrt(1) in QQbar
True
sage: sqrt(-2) in QQbar
True
sage: sqrt(-1) in QQbar
False

Can someone explain ?

Note that, however :

sage: [t[0] in QQbar for t in (x^2+1).roots(ring=QQbar)]
[True, True]