In the following C denotes the set of complex numbers with i = V-1 and No = {0, 1, 2,3..}. If z C and k e No, then z(z-1)-(3-k+1) if k>0, () { if k = 0. is called a binomial coefficient to be read as 'z choose k'. a) Find (), (), (). b) Let z C. Prove that 2 - k k+1k for all k E No. c) If z C, prove that (':)- () (* : ) - (:) %3D k +1 k+1 for all k E No. d) Prove the binomial formula. If z, w e C, then (z + w)" = E(") k=0 for all n e N. e) Is the binomial formula also true if n 0? [6,6,6,6,1] Question 2: a) Prove that the set Z of the integers is not bounded above and not bounded below.