State true or false with reason all from Complex Analysis a

State true or false with reason (all from Complex Analysis):-

(a) Power series has an antiderivative everywhere inside its disc of convergence

(c) There does not exist any analytic function f defined on C\\ {0} such that f \' (z) = 1/z

(d) If a mobius transformation T carries z₁ and z₂ into a same number w₁ then either z₁ = z₂ or else T is a constant map

Solution

(a) Power series has an antiderivative everywhere inside its disc of convergence. (TRUE)