Which of the following subsets of G CC are (i) open, (ii) connected, (iii) a domain? (a) G = {z € C; |z| < 2} \ {z € C; Rez = 0}, (b) G = {z € C; |2| < 2} n{z € C; Re z > 0}, (c) G = {z € C; |2| < 2} U {z € C; Re z > 0}, (d) G = {z € C; |2| < 2} \ {z € C; Re z = 0}. %3D

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Which of the following subsets of G CC are (i) open, (ii) connected, (iii) a domain?
(a) G = {z € C; |z| < 2} \ {z € C; Rez = 0},
(b) G = {z € C; |z| < 2}n{z € C; Re z > 0},
(c) G = {z € C; |z| < 2}U{z € C; Rez > 0},
(d) G = {z € C; |z| < 2} \ {z € C; Rez = 0}.
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Justify your answers.
Transcribed Image Text:Which of the following subsets of G CC are (i) open, (ii) connected, (iii) a domain? (a) G = {z € C; |z| < 2} \ {z € C; Rez = 0}, (b) G = {z € C; |z| < 2}n{z € C; Re z > 0}, (c) G = {z € C; |z| < 2}U{z € C; Rez > 0}, (d) G = {z € C; |z| < 2} \ {z € C; Rez = 0}. %3D %3D %3D %3D Justify your answers.
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