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)
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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,...
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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 =
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