Let D = {2 C {0}: < Arg z < D =...

 

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Let ㅠ π D₁ = {2 € C\ {0}: < Arg z < π D₂ = { € C: 0 ≤ Re(z) ≤ & 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. e) Find and sketch the image of D₂ under the mapping w = e²² Let ㅠ π D₁ = {2 € C\ {0}: < Arg z < π D₂ = { € C: 0 ≤ Re(z) ≤ & 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. e) Find and sketch the image of D₂ under the mapping w = e²²

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