Intuitively what is it if making a modification of a torus?

Question

It is well-known that if we have a equivalence relation in $\mathbb{R}^2$:$(z_1,z_2)\sim (z_1',z_2')$ iff
$$\begin{pmatrix} z_1'\\ z_2' \\ \end{pmatrix}=\begin{pmatrix} 1&0\\ 0&1 \\ \end{pmatrix}\begin{pmatrix} z_1\\ z_2 \\ \end{pmatrix}+\begin{pmatrix} a_1\\ a_2 \\ \end{pmatrix}$$ with nonzero constants $a_1,a_2\in\mathbb{R}$.Intuitively we get a torus.
Now let us make a small modification:$(z_1,z_2)\sim (z_1',z_2')$ iff
$$\begin{pmatrix} z_1'\\ z_2' \\ \end{pmatrix}=\begin{pmatrix} 1&\lambda\\ 0&1 \\ \end{pmatrix}\begin{pmatrix} z_1\\ z_2 \\ \end{pmatrix}+\begin{pmatrix} a_1\\ a_2 \\ \end{pmatrix}$$ with nonzero constants $a_1,a_2,\lambda\in\mathbb{R}$.Intuitively what is it?
Does your answer still hold when we replace $\mathbb{R}$ to $\mathbb{C}$?
Can you help me?Thank you very much!