fundamental groups of complement of lines in $\mathbb{C}^2$

fundamental groups of complement of lines in $\mathbb{C}^2$

Consider the 2-dimensional complex vector space $\mathbb{C}^2$. $H_1$ and
$H_2$ are the 1-dimensional subspace determined by $z_1+z_2=0$ and
$z_1-z_2=0$ respectively. How to compute the fundamental group and
homology groups of $\mathbb{C}^2\setminus(H_1\cup H_2)$ ? I need help.
Thanks a lot!