The factorization of 2 is fine -- factorizations are equivalent if they're off by a unit, and i is a unit.
By the same token, 1+i and 1-i are essentially the same prime, since you can multiply one by a unit to get the other. That's how we can get away with saying 2 is a power.
edit: Just noticed the sibling comment by mrkgnao, which is a very good overview of some of the technical nitty-gritty that goes into this.
By the same token, 1+i and 1-i are essentially the same prime, since you can multiply one by a unit to get the other. That's how we can get away with saying 2 is a power.
edit: Just noticed the sibling comment by mrkgnao, which is a very good overview of some of the technical nitty-gritty that goes into this.