complex projective line

Let $ℂ$ be the set of complex numbers. We define an equivalence relation on ${ℂ}^2-\{0,0\}$ by

$$(x1,y1)\sim (x2,y2)\iff \exists \lambda \in {ℂ}^{*}\lambda (x1,y1)=(x2,y2)$$(1)

The set ${ℂ}^2-\{0,0\}/\sim$ is a projective variety called the complex projective line.