Transformations (a) Consider the complex function f(z) = z. Find the image of the unit circle | z = 1 under the transformation of f. (b) Let f(z) = 2z. Find the image of a circle of diameter 1 with the center at the origin. of the line sorment connecting 1 and i under the
Transformations (a) Consider the complex function f(z) = z. Find the image of the unit circle | z = 1 under the transformation of f. (b) Let f(z) = 2z. Find the image of a circle of diameter 1 with the center at the origin. of the line sorment connecting 1 and i under the
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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Transcribed Image Text:Transformations (a) Consider the complex function f(z) = z. Find the image of the unit
circle | z = 1 under the transformation of f.
(b) Let f(z) = 2z. Find the image of a circle of diameter 1 with the center at the origin.
(c) Let f(z) 2³. Determine the image of the line segment connecting 1 and i under the
transformation f.
(d) Find the image of the circle | z | 2= 4 under the transformation f(z) = iz + 1.
(e) Find the image of the line y - x = -1 under f(2)= and show it graphically.
-
|z|²
=
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