10. Find the image of the following sets under the mapping w = z¹/². (a) {re: r> I and /3 < 0 < π/2} (b) {re: 1
10. Find the image of the following sets under the mapping w = z¹/². (a) {re: r> I and /3 < 0 < π/2} (b) {re: 1
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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Question 10 from the Complex Analysis for Mathematics and Engineering
Transcribed Image Text:be used
7. Sketch the set of points satisfying the following relations.
(a) Re(²) > 4
(b) Im(²) > 6
8. Show that the region in the right half plane that lies to the right of th
x² - y² = 1 is mapped onto the right half plane Re(w) > 1 by the mappin
9. Show that the image of the line x = 4 under the mapping w = z¹/2 is the
of the hyperbola u² - y² = 4.
10.
Find the image of the following sets under the mapping w = z¹/².
(a) {re: r>1 and /3 < 0 < π/2}
(b) {re: 1 <r < 9 and 0 < 0 < 2π/3}
(c) {re: r <4 and - < 0 < π/2}
11. Find the image of the right half plane Re(z) > 1 under the mapping w = 2
12. Show that the infinite strip 2 < y < 6 is mapped onto the region in the f
that lies between the hyperbolas uv = 1 and uv = 3 by the mapping w =
13. Find the image of the region in the first quadrant that lies between the
xy = // and xy 4 under the mapping w = z².
=
14. Show that the region in the z plane that lies to the right of the parabola x
is mapped onto the right half plane Re(w) > 2 by the mapping w = z2. H
inverse mapping z = w².
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