Let π D₁ = {z € C\{0} : < Arg z < 4 D₂ = {z € C: 0 ≤ Re(2) ≤ ½ & 0 ≤ Im(2) ≤ 1}. a) Sketch D₁ and D₂ on separate Argand diagrams and for each set state whether it is a domain. Explain your answer. b) Find and sketch the image of D₁ under the mapping w = 1. c) Find and sketch the image of D₂ under the mapping w = ¹². eiz
Let π D₁ = {z € C\{0} : < Arg z < 4 D₂ = {z € C: 0 ≤ Re(2) ≤ ½ & 0 ≤ Im(2) ≤ 1}. a) Sketch D₁ and D₂ on separate Argand diagrams and for each set state whether it is a domain. Explain your answer. b) Find and sketch the image of D₁ under the mapping w = 1. c) Find and sketch the image of D₂ under the mapping w = ¹². eiz
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let
π
D₁ = {z € C\{0} : < Arg z <
4
π
D₂ = {z € C : 0 ≤ Re(z) ≤ & 0 ≤ Im(z) ≤ 1}.
a) Sketch D₁ and D₂ on separate Argand diagrams and for each set
state whether it is a domain. Explain your answer.
b) Find and sketch the image of D₁ under the mapping w
=
1.
c) Find and sketch the image of D₂ under the mapping w = ¹².
eiz
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