Question 2. (6,5,6,4,4] a) If w is a complex sixth root of unity, and w? +...

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Question 2. (6,5,6,4,4] a) If w is a complex sixth root of unity, and w? + 1 w³, show that w² – w +1 = 0. b) Show that (1+ i)" – (1 – i)" is imaginary for any positive integer n. c) Show that the set of all limit points of any subset of C is closed. d) Find the closure of A = {z € C : |2 – i| < 2}. e) Determine whether the set B = {z EC : Im(z) # 0} is convex or not. Question 2. (6,5,6,4,4] a) If w is a complex sixth root of unity, and w? + 1 w³, show that w² – w +1 = 0. b) Show that (1+ i)" – (1 – i)" is imaginary for any positive integer n. c) Show that the set of all limit points of any subset of C is closed. d) Find the closure of A = {z € C : |2 – i| < 2}. e) Determine whether the set B = {z EC : Im(z) # 0} is convex or not.