7.(a) Let X = {z € C: 0 < Arg(z) < π/3} and let ƒ: X → C be the function defined on X by f(z) = 2³. Determine the range of f. (I.e., determine which complex numbers can be expressed as f(z) for some z € X.) (b) Let Y = {z € C: 0 < |z] < 1} and let g: Y → C be the function defined on Y by g(z) = 1/2. Determine the range of g.
7.(a) Let X = {z € C: 0 < Arg(z) < π/3} and let ƒ: X → C be the function defined on X by f(z) = 2³. Determine the range of f. (I.e., determine which complex numbers can be expressed as f(z) for some z € X.) (b) Let Y = {z € C: 0 < |z] < 1} and let g: Y → C be the function defined on Y by g(z) = 1/2. Determine the range of g.
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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![7.(a) Let X = {z € C: 0 < Arg(z) < π/3} and let ƒ: X → C be the function defined on X by f(z) = 2³.
Determine the range of f. (I.e., determine which complex numbers can be expressed as f(z) for
some z € X.)
(b) Let Y = {z € C: 0 < |z] < 1} and let g: Y → C be the function defined on Y by g(z) = 1/2.
Determine the range of g.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F490cbcd2-ad81-426b-824f-903aced284ba%2Fe22decd0-500c-4b51-8a1f-cf0d86915d8e%2Fwmn7jj8_processed.png&w=3840&q=75)
Transcribed Image Text:7.(a) Let X = {z € C: 0 < Arg(z) < π/3} and let ƒ: X → C be the function defined on X by f(z) = 2³.
Determine the range of f. (I.e., determine which complex numbers can be expressed as f(z) for
some z € X.)
(b) Let Y = {z € C: 0 < |z] < 1} and let g: Y → C be the function defined on Y by g(z) = 1/2.
Determine the range of g.
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