V is a vector space over real numbers, u is a vector belongs to V. u=(a1, a2), where a1 and a2 are complex number. Is this possible.

Question

anonymous · Answer

check the sets of numbers, real numbers contain complex numbers

anonymous · Answer

My question is that is this possible, that a vector space over the real number can contain the complex number as elements of the vector..

anonymous · Answer

It it impossible.

anonymous · Answer

Then it would, by definition, be a vector space over the field of complex numbers.

anonymous · Answer

@JonW : Field is said regarding the scalar or the elements of the vector in the vector space.

All the places I have searched , I have found field is regarding the scalars ; nothing is written related to elements of the vector in the vector space.
Here, 
 elements means: v=(a1,a2,a3)
 a1, a2  & a3 are the elements of vector v.

anonymous · Answer

Real numbers are a subset of the complex numbers and not the other war around. So I think its impossible.