(a) Determine the disk of convergence of the power series
(n^5)(z-3i)^n/4^n) for n=1 to infinity
(b) Use taylore theorem to determine the taylor series about 2i for the functio f(z) = Log(z+i), giving an expression for the general term of teh series. Also, state the largest open disk on which the function f is represented by this taylor series.
(c) Find the taylor series about 0 for each of the following functions:
(i) f(z) = (e^2z)Coshz (up to the terms in z^3)
(ii) f(z) - Log(2-cosz) (up to the terms in z^6)
(d) Let the function f be entire and suppose that
f(i/n) = -(2/n^3) for all n subset N
show that f(z) = - 2iz^3
Thankyou