For each given set S and the mapping f(z) in [(a)-(d)], answer the following questions[(i)-(ii)]: (i) Sketch the set S and determine if it is open/closed/domain.Justify your answer. (ii) Sketch the image of the set S under the mapping f(z) and and determine if the image is open/closed/domain. (a) the set S = <√√2, < Arg(2) < under the mapping f(z) = z² e¹7 + 2 4 (b) the set Re(z) ≥ 0 and Im(z) ≥ 0 under the mapping f(2)= z²+2+4i under the mapping f(z) = 2iz² (c) the set S = {z € C: 1 ≤|z| ≤ 2,7 < Arg(z) < (d) The line Im(z) = 5 under the mapping f(z) = 2² +2