Multiplying a vector by a scalar

Plotting numbers on the complex plane

SOLVED: Let's be the set of column vectors with two complex number entries with the following definitions: vector addition and scalar multiplication. [X,Y] = [Z,W] [S,T] where X,Y,Z,W are in C and S is in R vector space over the field of real numbers. Why? Why not? Is V a vector space? Yes, because all 10 vector space axioms are satisfied. No, because the additive closure axiom is not satisfied, though the zero axiom is satisfied. No, because neither the additive inverse axiom nor the zero axi