Let A = {z = x + y = C: ≥1}. (1.1) Show that A = {z = x+iy € C: y ≥ 1; (x, y) = (0,4)}. (1.2) Sketch the set A. (1.3) Is z = 5+i a boundary point of A? Provide reasons for your answer. (1.4) Is A open, closed, both or neither? Provide reasons for your answer.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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= { z = x + iy € C : | 2 + ²i | ≥ 1}.
(1.1) Show that A = {z = x+iy € C: y ≥ 1; (x, y) ‡ (0,4)}.
Let A =
(1.2) Sketch the set A.
(1.3) Is z = 5 +i a boundary point of A? Provide reasons for your answer.
(1.4) Is A open, closed, both or neither? Provide reasons for your answer.
Transcribed Image Text:= { z = x + iy € C : | 2 + ²i | ≥ 1}. (1.1) Show that A = {z = x+iy € C: y ≥ 1; (x, y) ‡ (0,4)}. Let A = (1.2) Sketch the set A. (1.3) Is z = 5 +i a boundary point of A? Provide reasons for your answer. (1.4) Is A open, closed, both or neither? Provide reasons for your answer.
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