>>3
>what did he mean by this?
1) All he's doing is writing [math]\mathbb{C} = \{ a + bi \mid a, b \in \mathbb{R} \}[/math] as 2-tuples [math](a, b)[/math].  The first paragraph is stating something that is otherwise obvious - the subset of complex numbers that have no imaginary part are exactly the real numbers.  What separates. [math]\mathbb{C}[/math] from [math]\mathbb{R}^2[/math] with the obvious usual operations entrywise is that imaginary multiplication is different.