In general a vector space consists of vectors with scalar multipliers. In two dimensions vectors are of the form (x,y) where x and y are numbers (scalars). For a real vector space x and y will be real numbers and the scalars are real numbers, while for a complex vector space x and y will be complex numbers and the scalars may be complex.. Vectors can be added or subtracted and multiplied by scalars.

For example Let (x,y) and (u,v) be vectors and a and b scalars, then
a(x,y) + b(u,v) = (ax+bu,ay+bv).