Exercise 3. Sketch the following subsets of C, and say which of them are open in C and closedin C.1. A = {z € C : 1 <|z|<3, Im(2)>0};12. (*) B={C: |exp(z)| < 1}.Hint Recall that exp(x + y) = exp(r) (cos(y) + i sin(y)).

Set A = {z ∈ C : 1 < |z| < 3, Im(z) ≥ 0} Step 1: Understand the components z is a complex…

Answered: Exercise 3. Sketch the following…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 11E

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Show that exp(2²)| ≤ exp(2²) < for all = E C.

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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)).