For the Simply Connected Equivalence Theorem below, show the following: (i) (d) implies (e) (ii) (g) implies (h) Simply Connected Equivalence Theorem Let Ω be a region in C. Then the following are equivalent. (a) Ω is simply connected. (b) Wγ​(z)=0 for every closed curve γ⊂Ω and every z∈/Ω. (c) C[infinity]​\Ω is connected. (d) If f is holomorphic on Ω, then there is a sequence of polynomials that converges locally uniformly to f. (e) If f is holomorphic on Ω, then ∫γ​f(z)dz=0 for all closed curves γ⊂Ω. (f) Every holomorphic function on Ω has a primitive. (g) If f is a nonvanishing holomorphic function on Ω, there is a holomorphic function g such that f(z)=eg(z). (h) If f is a nonvanishing holomorphic function on Ω, there is a holomorphic function h such that f(z)=(h(z))2. (i) Ω is homeomorphic to the unit disc. (j) If u:Ω→R is harmonic, then it is the real part of some holomorphic function on Ω.