In the article he says there is a model of ZFC in which the complex numbers have indistinguishable square roots of -1. Thus that model presumably does not allow for a rigid coordinate view of complex numbers.
It just means that there are two indistinguishable coordinate views a + bi and a - bi, and you can pick whichever you prefer.
It just means that there are two indistinguishable coordinate views a + bi and a - bi, and you can pick whichever you prefer.