Let G (s) = 5-4 s+ 2 be a function in complex variable s = o + jw. (a) Determine |G(s) | and Z(G(s)) as functions of o and w. [Hint: it may be useful to know that for any complex pair Z1, Z2 the following identities hold : 21 1211 1zz1 and _ ) = 421 - ZZ2. (b) Determine |G(s) | and Z(G(s)) at s = 1 + j4. (c) Determine |G(s)| at s = 3 + j1. N +1 ifz = 1 (a) Prove that the solution to the finite sum _ _ z" is given by 1-2 (N+1) if z # 1' 1-z (b) Prove that the solution to the finite sum _n=m Z" is given by N- m+1 ifz = 1 z m 1-2[N-m+1) if z # 1" 1-2 [Hint: use a) to derive b); Note that _n=m z" = 2n'=0 Z N-m -n'tm _ zmyN-m 2n'=0 Zn']