- #1
Mdhiggenz
- 327
- 1
Homework Statement
We are to show that the set C of complex numbers, with scalar multiplication de ned
by α(a + bi) = αa + αbi and addition de fined by (a + bi) + (c + di) = (a + c) + (b + d)i,
satis es the eight axioms of a vector space
I have a few questions about this problem,
What is the term i? is it just a fancy way of saying a2
Can we think of these as vectors, for instance (a+bi)
is the vector X where a is x1 and bi is x2?
Also I was trying to prove the third axiom which states there exist an element 0 in V such that x+0=x for each xεV.
My logic was let (a+bi)= vector X and (c+di)= Vector Y
X+Y=X
X-X+Y=X-X
Y=0
thus X+Y=X
Thanks for the help guys.