First Chern class of a tensor product of complex line bundles ($c_1(L\otimes M)=c_1(L)+c_1(M)$)

The First Chern class turns the tensor product of vector bundles of complex line bundles into addition in integral cohomology. This follows by computing the universal complex line bundle on the product of two Complex projective spaces and restricting to each factor. The proof retains torsion elements, which differential forms alone cannot detect.