(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a basis for [tex]V=\mathbb{C}^1[/tex], where the field is the real numbers.

3. The attempt at a solution

I'd say [tex]\vec{e}_1=(1,0), \vec{e}_2=(i,0)[/tex] is a basis, because it seems to me that [tex] \vec{u}=a+bi \in V[/tex] can be written as

[tex]a(1,0)+b(i,0)=(a,0)+(bi,0)=\mathbf{(a+bi,0)=a+bi+0=a+bi=\vec{u} }[/tex], where a and b are real.

I'm a bit unsure about the bolded part, though. Is it correct?

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# Homework Help: Basis of a real vector space with complex vectors

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