If V is a subset of C^3 consists of those vectors (x1, x2, x3) for which x1+ i x2 =0
is V a vector space?

Question

If V is a subset of C^3 consists of those vectors (x1, x2, x3) for which x1+ i x2 =0
is V a vector space?

anonymous · Answer

Hmmmm, not completely sure.

loser66 · Answer

I have it closed under addition 
to multiplication, can I take i as a scalar to test?

loser66 · Answer

since x 1+i x2 =0 --> x1= -ix2
I have the form of the vectors is (-ix2, x2,x3) and then + axiom is closed

loser66 · Answer

to k is real, * asiom closed, too. 
I try to find out a counter example with the case k =i

loser66 · Answer

Is it legal to do that? (to "treat" i as a constant?) If it is legal, then V is a vector space, too.

anonymous · Answer

I'm not sure how bases work in the complex plane.  Don't you need twice as many to account for two degrees of freedom?

anonymous · Answer

You should be able to treat $i$ as a constant.  I'm under the impression $c\in \mathbb{C}$.  And so you can have any $a+bi$ as a constant scalar.

loser66 · Answer

Got you, thank you very much. ( still have a bunch of questions) :)

anonymous · Answer

if $c=0$ then would it have the 0 vector?