Q5. Let V= : x,y € ER}. In this problem we will view V as a vector space over C, with addition and scalar multiplication defined by [az - by D]+=+M

and (a+ib) [*] = bx + ay So vector addition is the usual addition on R² but now we have a way to multiply by complex scalars. In this problem, you may take it for granted that these operations do indeed turn V into a vector space over C. (a) Compute i [] [Aside: Do you recognize what is being done geometrically? This may help you solve the next part.] (b) Find a basis for V and hence determine dim(V). (c) Prove that V is isomorphic to C. [Aside: Contrast this problem with Conceptual Q11 in the Chapter 1 Practice Problems, where we looked at how to view C² as a vector space over R. In this problem we've turned R2 into a vector space over C!]