12.1. For each of the following domains, determine whether it is simply connected, multiply connected, or neither (not connected): (a). A = {2:0< |2z-1|<3}, (b). B = {2: Argz #0}, (c). C= {z: z-i>1, 2-3 > 3 and 2 <10}, (d). D= {z: Im z # 0}, (e). E = {2:12 <1 and Rez <0}, (f). F= C-{x+iy: 0≤x≤3}.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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12.1. For each of the following domains, determine whether it is simply
connected, multiply connected, or neither (not connected):
(a). A = {2:0< |2z - 1|<3},
(b). B = {2: Arg z #0},
(c). C= {z: z-i| > 1,
(d). D = {2: Im z #0},
2-3 > 3 and 2<10},
(e). E = {2:|2|<1 and Rez < 0},
(f). F= C-{x+iy: 0≤x≤3}.
Transcribed Image Text:12.1. For each of the following domains, determine whether it is simply connected, multiply connected, or neither (not connected): (a). A = {2:0< |2z - 1|<3}, (b). B = {2: Arg z #0}, (c). C= {z: z-i| > 1, (d). D = {2: Im z #0}, 2-3 > 3 and 2<10}, (e). E = {2:|2|<1 and Rez < 0}, (f). F= C-{x+iy: 0≤x≤3}.
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