Find the dimension and a basis for each vector space.

Question

GIven that $\mathbb{C}$ is the complex field , $\mathbb{R}$ is the real field. Find the dimension and a basis for each vector space.

My attempts : I know that $V$ is a vector space over $F$ if the

$\lambda v \in V$ for all $\lambda \in F$ and $v \in V$

Now here, I take for option 1) basis will be $\{1,i\}$ , dimension is $2$.i had confused about option $2$

Is my answer is correct / not correct ?

Any hints/solution will be appreciated.

Thanks in advance

soory ,,i thinks both have same basis, so their dimension will be same @DietrichBurde — jasmine, Jun 19 '18 at 08:38

score 0 · Accepted Answer · answered Jun 19 '18 at 08:48

$\mathbb{V}$ is a vector space over $\mathbb{F}$ if the

$\lambda v \in \mathbb{V}$ for all $\lambda \in \mathbb{F}$ and $v \in \mathbb{V}$

For option $2.)$ i $\in \mathbb{C}$ and $1$ $\in$ $\mathbb{R}$ but $ 1.i =i$ not belong $\mathbb{R}$

1 Answers1