Let H = {2€ C. Re(2) >0} be the right half-plane. Let 8(2)= exp( + Lag (2)) be the principal branch of 2² in D* = ( \(-00,0). a) Show that s maps D² into H (₁0) CH). b) Suppose of is entire and maps C to Dr. That is (-es, c) is not in the (-00, c) is not in the range of f. Show that f must be constant. (Hint: Consider 3 (t) = x(f(x)) and show that if ZEH, then 12+1121).