A subset U of Cn is called a complex subspace of Cn if it contains 0 and

Question:

A subset U of Cn is called a complex subspace of Cn if it contains 0 and if, given Z and W in U, both Z + W and zZ lie in U (z any complex number). In each case, determine whether U is a complex subspace of (a) U = {(w, 2w, a) | w in C, a in R}
(b) U = {(v + w, v - 2w, v) | v, w in C}