Complex variables-taylor series

Question

Assignment:

Obtain the Taylor series,

e^z = e Σ^∞_n=0 (z-1)ⁿ/n! (|Z-1| < ∞)

for the function f(Z) = e^z by

a) using f⁽ⁿ⁾ (1) (n = 0,1,2...);
b) writing e^z = e^z-1e.

Provide complete and step by step solution for the question and show calculations and use formulas.