Example 10.3. Let S be the vertical strip S = {z = r+iy : 2< x < 3}. Find the image of S under the mapping w = f(z) = z². Since w = y? + 2ixy, a point (x, y) of the z-plane maps into (u, v) = (x² – y², 2xy) in the w-plane. Now, eliminating y from the equations u = v = 2xy, we get x2 – y? and v2 U = x | 4.x2 *

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
Question
I need the answer as soon as possible
Example 10.3. Let S be the vertical strip S = {z = x+iy : 2 < x < 3}.
Find the image of S under the mapping w
y? + 2ixy, a point (x, y) of the z-plane maps into (u, v) = (x2 – y?, 2xy)
in the w-plane. Now, eliminating y from the equations u =
2xy, we get
f(z) = z2. Since w =
x2
x2 – y? and
v =
v2
= a2
4.x2
U =
Transcribed Image Text:Example 10.3. Let S be the vertical strip S = {z = x+iy : 2 < x < 3}. Find the image of S under the mapping w y? + 2ixy, a point (x, y) of the z-plane maps into (u, v) = (x2 – y?, 2xy) in the w-plane. Now, eliminating y from the equations u = 2xy, we get f(z) = z2. Since w = x2 x2 – y? and v = v2 = a2 4.x2 U =
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education