Hello, I am having a hard time understanding what is meant by this notation:

2. Are the following vector spaces?

(iii) , (over and with the usual addition and scalar multiplication of functions).

(The is the complex numbers; I'm not sure how to do that in Latex)

The part that's comfusing me is the overline... does that mean that is a vector? Do the reals map to the complexes as a vector because it's an ordered pair with as a complex number? Thank you for any help!