Question

how to prove that set of real no r is a sub space of complex no vector space c, i need a proof kind of a thing

Answer 1

Inorder to prove anything to be a subspace of vector space,
It should be defined under addition and scalar multiplication.
ADDITION:
let a,b be two real no.s
a+b is also a real no.It can be considered as complex no. where the imaginary part is zero.
hence a+b belongs to C(complex no.s)
therefore,it is defined on addition
SCALAR MULTIPLICATION:
c*a=ca belongs to the set of real no.s. Again it can be considered as a complex no with it's imaginary part zero.
hence ca belongs to C
therefor,it is defined on scalar multiplication.
Thus a subspace.
P.S..This is what I know

Answer 2

thanx

Answer 3

:)