We have the lattice $L = \{m_1w_1 + m_2w_2 \mid m_1, m_2 \in \mathbb{Z}, w_1, w_2 \in \mathbb{C}\}$. We want to construct a homeomorphism between $\mathbb{C}/L$ and $S^1\times S^1$. I've read that the function $f(z)= (e^{2\pi ai},e^{2\pi bi})$ with $z=aw_1 +bw_2$ could be an option. Can someone explain to me in more detail why this function gives us the homeomorphism we want?
Thank you.