A Platonist with respect to what?
If you're a platonist with respect to sets, the real number 2 and the complex number 2 are in fact different. For the reals, one proceeds via, say, Dedekind cuts, for the complex numbers we realize the underlying set as R x R, then proceed to define addition and multiplication. In fact, 2 as a natural, integer, rational, real, complex, etc... are all in fact different- although there is a natural (set)-embedding from each structure to its superstructures.
This may seem strange, but its a consequence of Platonism + using, say, ZFC as a foundation.
Some (say Beneceraff) find this strange. You'll want to think of structuralism for a different perspective on the matter.
(a): by platonism, I mean something along the lines of existence, abstraction, and independence holding for "the" mathematical ontology. This may not be what the historical Plato thought, see Landry for further discussion. Nonetheless, this is typically what is meant in the literature today.
(b): Of course, once can also be a platonist about structures (ante rem).
(c): for an alternate platonistic view that does not priviledge any one set theoretic universe, one can also consider Balagauers plenitudinuous platonism. It consciously draws on model theoretic concepts, so that both the real and complex number two "satisfy" being the number two. Thus, there can be multiple number twos that exist independently of us.