MATH2036-E1A& LEVEL& 2& MODULE, SPRING& SEMESTER& 2022-2023COMPLEX& FUNCTIONS1. (A) Consider The Seta = {Z = X + Iy : |Y| &< |X| + 1}I) Sketch A And Show That A Is Open. [6 Marks]Ii) Show That A Is A Star-Domain. [6 Marks](B) Where Is The Functionf(X + Iy) = (X3y — Xy3) + Ix2y2complex Di

MATH2036 COMPLEX FUNCTIONS FINAL EXAM A LEVEL 2 MODULE, 2021-2022Problem 1. (A) A Set A ⊂ C Is Called Convex If ∀X, Y ∈ A And ∀Λ ∈ [0, 1] [12 Marks](1 − Λ)X + Λy ∈ A.Show That If Domains An, N = 1, 2, . . . Are Convex And ∩∞N=1An = ∅ Then The Set ∪∞N=1An Is A Starshape-Domain.(B) Let The Function F