# Complex/Real Vector Spaces

## Homework Statement

Hello, I'm having a little difficulty with this proof.
Prove: If V is a complex vector space, then V is also a real vector space.

## Homework Equations

Definition 1: A vector space V is called a real vector space if the scalars are real numbers.
Definition 2: A vector space V is called a complex vector space if the scalars are complex numbers.

## The Attempt at a Solution

I've tried a proof by contradiction saying that "V is a complex vector space and V is not a real vector space." Can't seem to find any sort of contradiction throughout my argument though.

Dick
Homework Helper
It's good that you didn't find any contradictions, because there aren't any. The set of vectors in a complex vector space with complex scalars are also a vector space over the reals. Just try to prove it directly. What things do you need to prove?

I just need to develop a proof using the vector space axioms and the two definitions listed above that if V is a complex vector space, then V is also a real vector space. Not sure how to go about proving it directly though....

Dick