Is the space of n-tuples of complex numbers a vector space over the reals?

[iwonde]

Homework Statement

Let V = {(a1,a2,...an): ai $$\in$$ C for i = 1,2,...n}; Is V a vector space over the field of real numbers with the operations of coordinatewise addition and multiplication?

Homework Equations

I know that V is a vector space over C.

The Attempt at a Solution

I actually don't really understand the problem, especially what it means by vector space over the field of real numbers. Any suggestions would be great. Thanks.

 

[tiny-tim]

Hi iwonde!

It just means that you must prove that it satsifies the axioms of a vector space.

See http://en.wikipedia.org/wiki/Vector_space#Definition