Given a complex number w, define TU: C → C by Tz ,(z) = wz for all z in C.
(a) Show that Tu, is a linear operator for each w in C, viewing C as a real vector space.
(b) If B is any ordered basis of C, define S: C -> M22 by S(w) = Mb(Tu.) for all w in C. Show that S is a one-to-one linear transformation with the additional property that S(wv) = S(w) S(v) holds for all w and v in C.