Complex Projective Plane

The set $\Bbb{P}^2$ is the set of all Equivalence Classes $[a,b,c]$ of ordered triples $(a,b,c)\in\Bbb{C}^3 \backslash(0,0,0)$ under the equivalence relation $(a,b,c)\sim (a',b',c')$ if $(a,b,c)=(\lambda a', \lambda b', \lambda c')$ for some Nonzero Complex Number $\lambda$.