Question

nared 1.27. Sketch the sets defined by the following constraints and determine whether they closed, or neither; bounded; connected. are open, (d) |z 1+z+1 = 2 (a) |z+31<2 (b) [Im(z)< 1 (c) 0 (f) |2 Re(z)+1 z-1< 2 1.28. What are the boundaries of the sets in the previous exercise?

Answer 1

(a) 1 2+ 3 2 2- -3) < 2 the on o a equati entu -3+o Tis irde and is with sadius and Copen cirde, that all inside enclading it) 4 2 3 This is conne cted open bounded and

<I (b) tonne cted unbounded hot open (tts complemunt twiu not k cleard the 4t and not it doeint include the dary)

o<2-1 2 c) the oannulus with (1,0): This feshl ts centu at 2- not opeh This boundeol is omplununt the hot dlored (its is not rdbounday loard inchidud) and hole) ennectd not hal a

2t1 = 2 (d 2-1 () ut 2. liv) 티리 원리 팀나리 21 t 2 2 2. 2-1= 1리1+| - 2지 2- 412-11+12-1 4 - get 4-4 (2-11) from iu ) wp + +X 22 4x= 니-4 |211 2-1 1- -2) wei g스 14112 N 1리+1-2개 = (i-a).

Date get y(v) we 2 (-3) -7) +1-22 2 +1-2x 1- 22+ the heal (x). ie TWis aris duay unbounded, open (its dosedemectd 4t is emplement s nme dtid) kaing Path co