What are the StiefelWhitney classes of complex projective spaces?
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It follows from the Whitney sum formula that $c(T_{\mathbf{C}P^n}) = (1+z)^{n+1}$, where $z \in H^2(\mathbf{C}P^n,\mathbf{Z})$ is the generator corresponding to the canonical bundle. (I assume you meant the Chern classes; for the StiefelWhitney of a complex vector bundle restricted to a real vector bundle, $w_{2i}$ is the mod$2$ reduction of $c_i$; and for the odd StiefelWhitney classes note that $H^{2i+1}(\mathbf{C}P^n) = 0$) 

