I am trying to prove the following from Milnor and Stasheff but haven't been able to crack it. The hint seems to suggest that this can be done completely using the total chern classes but I haven't been able to do so?
2026-03-26 01:26:53.1774488413
Relation between Pontryagin classes and Chern classes, confusion with proof
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All that’s going on here is the isomorphism $$\omega_{\Bbb R} \otimes\Bbb C \cong \omega\oplus\overline\omega$$ and the fact that $c(E\oplus F)=c(E)c(F)$.