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Exercise 3. Sketch the following subsets of C, and say which of them are open in C and closed in C. 1. A = {z € C : 1 <|z|<3, Im(2)>0}; 1 2. (*) B={C: |exp(z)| < 1}. Hint Recall that exp(x + y) = exp(r) (cos(y) + i sin(y)).

Exercise 3. Sketch the following subsets of C, and say which of them are open in C and closed in C. 1. A = {z € C : 1 <|z|<3, Im(2)>0}; 1 2. (*) B={C: |exp(z)| < 1}. Hint Recall that exp(x + y) = exp(r) (cos(y) + i sin(y)).

Advanced Engineering Mathematics
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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Exercise 3. Sketch the following subsets of C, and say which of them are open in C and closed in C. 1. A = {z € C : 1 <|z|<3, Im(2)>0}; 1 2. (*) B={C: |exp(z)| < 1}. Hint Recall that exp(x + y) = exp(r) (cos(y) + i sin(y)).
Transcribed Image Text:Exercise 3. Sketch the following subsets of C, and say which of them are open in C and closed in C. 1. A = {z € C : 1 <|z|<3, Im(2)>0}; 1 2. (*) B={C: |exp(z)| < 1}. Hint Recall that exp(x + y) = exp(r) (cos(y) + i sin(y)).
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