Vector Space Dimension: Real vs Complex Coefficients

[ak123456]

Homework Statement

Let V be a vector space over C of dimenson n . We view V also as a vector space over R by restricting the scalar multiplication of C on V to R .Show that dimR(V) = 2n

Homework Equations

The Attempt at a Solution

I have to show that if x1,...xn form a basis of V over C then x1,...xn ix1,...ixn form a basis of V over R
but i still confuse about it

 

[tiny-tim]

Hi ak123456!

I have to show that if x1,...xn form a basis of V over C then x1,...xn ix1,...ixn form a basis of V over R

That's right!

First prove that they are independent.

Then start with any element of V, and prove that it is a combination of them, with real coefficients