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1. Sketch the following sets and determine which are domains: (a) |z−2+i| ≤ 1; (c) Imz > 1; (e) 0 ≤ arg z ≤ л/4 (z ‡ 0); Ans. (b), (c) are domains. (b) |2z+3| > 4; (d) Imz = 1; (f) | z − 4| ≥ |z. -- 2. Which sets in Exercise 1 are neither open nor closed? Ans. (e).

1. Sketch the following sets and determine which are domains: (a) |z−2+i| ≤ 1; (c) Imz > 1; (e) 0 ≤ arg z ≤ л/4 (z ‡ 0); Ans. (b), (c) are domains. (b) |2z+3| > 4; (d) Imz = 1; (f) | z − 4| ≥ |z. -- 2. Which sets in Exercise 1 are neither open nor closed? Ans. (e).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 50E
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So let's see, the first one is the first one, and the second one is based on the first one！！

1. Sketch the following sets and determine which are domains: (a) |z−2+i| ≤ 1; (c) Imz > 1; (e) 0 ≤ arg z ≤ л/4 (z ‡ 0); Ans. (b), (c) are domains. (b) |2z+3| > 4; (d) Imz = 1; (f) | z − 4| ≥ |z. -- 2. Which sets in Exercise 1 are neither open nor closed? Ans. (e).
Transcribed Image Text:1. Sketch the following sets and determine which are domains: (a) |z−2+i| ≤ 1; (c) Imz > 1; (e) 0 ≤ arg z ≤ л/4 (z ‡ 0); Ans. (b), (c) are domains. (b) |2z+3| > 4; (d) Imz = 1; (f) | z − 4| ≥ |z. -- 2. Which sets in Exercise 1 are neither open nor closed? Ans. (e).
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