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## Homework Statement

Let {e

_{1},...,e

^{n}} be a basis for a complex vector space X. Find a basis for X regarded as a real vector space. What is the dimension of X in either case?

## Homework Equations

## The Attempt at a Solution

I'm really not sure where to begin with this question.

Are the e

_{j}'s something like (i, 0, 0,...), (0,i,0,...)?

If so, could we take {ie

_{1},....,ie

_{n}} as the basis for X regarded as a real vector space?

Also, I think that the dimension in either case is n. Does anyone know if that is correct?

Thank you very much.