# Math Help - Space and dimension

1. ## Space and dimension

Let V be vector space with dimension of $n$ above C (complex plane). Now we look at him (V) like vector space above R. What his dimension above R?

2. Try constructing $\mathbb{C}$ (the complex plane) as a vector field using elements of $\mathbb{R}$.

Conclude the relation between them from the above.

3. So the dimension is 2n or I missing something...?

4. help...

5. Originally Posted by Also sprach Zarathustra
So the dimension is 2n or I missing something...?
Yes, since we can "construct" every element in $\mathbb{C}$ using 2 elements of $\mathbb{R}$, we may conclude that the dimension of a vector space spanned over $\mathbb{R}$ is twice than of the vector space spanned over $\mathbb{C}$.