Consider the function f(z) = 1/z(z - 2)(z² + 1)
(a) Give a closed form expression (as simplified as you can) for the Laurent coefficients when f(z) is expanded in a form valid near the origin.
(b) Give the coefficients c₋₁, c₀, c₁ in a Laurent expansion for f(z) around the origin, valid far out from the origin.
(c) Give the similar three coefficients c₋₁, c₀, c₁ for a Laurent expansion valid in the vicinity of z = a.