Dimension of Complex Vector Spaces over R?

[gtfitzpatrick]

Homework Statement

C is a 1-dim comples space. What is its dimesion when regarded a vector space over R

The Attempt at a Solution

if the complex vector space is dim 1 then the real part must = 0 so therefore when viewed over R the dimension must be 0 as well

 

[micromass]

if the complex vector space is dim 1 then the real part must = 0 so therefore when viewed over R the dimension must be 0 as well

Could you elaborate on this, since I don't understand your reasoning at all...
You know that the only 0-dimensional spaces is {0}, right? So there's no way C could have dimension 0...

 

[gtfitzpatrick]

sorry, i should have said a complex vector is dim 2 when viewed over R, but in this case its dim is 1 so the real part = 0. therefore when view over R only the complex part existins so when viewed over R is dimension is also 1?