Notation question: $R(A)=\mathbb{C}^2$ with $A\in End(\mathbb{R}^2)$

Question

I have a map, represented by the matrix $A=\left(\begin{array}{ll}1 & 0 \\1 & 1\end{array}\right)=End(\mathbb{R}^2)$.
My teacher wrote in his lecture notes that because it is invertible, we can conclude that $R(A)=\mathbb{C}^2$. To me it looks like he means that the range of the map is $\mathbb{C}^2$ with the complex part of all imaginary numbers equal to zero, which seems a bit odd when he defined $A\in End(\mathbb{R}^2)$. Am I correct, or does $\mathbb{C}$ not denote the complex numbers in this case?

Answer 1

We don't have your notes, but yes, the most likely interpretation is that this is a typo for $\mathbb{R}^2$.