250 (z - i) j Series Representations for Analy zo = i (d) 1- z = 1 0 (1 - i)j+1' Zo = 0 5.2 Tay (e) Log(1 - z) = 7. Ve (f) 23 = 1+3(2-1)+3(2-1)2+(2-1)3, 20 = 1 4. Determine the disks over which the Taylor expansions in Prob. 1 are you 3. Let f (z) = ER -j=0 ajz' be the Maclaurin expansion of a function f(z) the origin. Prove each of the following statements. 8. (a) Cajz2) is the Maclaurin expansion of g(z) := f (z2). 1=0 0O _ ajciz is the Maclaurin expansion of h(z) := f(cz). j=0 9. 10 (c) _ ajzm+ is the Maclaurin expansion of H (z) := z' f(z). 11 bad tine j=0 (d) j=0 Laj (z - zo)' is the Taylor expansion of G(z) := f (Z - zo) around, 4. Let a be a complex number. Show that if (1 + z)" is taken as ed Log(Itz) 121