Let T be the contour given by the following parameterisation if 0 ≤ t ≤ 1 if 1 ≤ t ≤2 if 2 ≤ t ≤ 3. z(t) = x(t) + iy(t) = = (1) Sketch the contour T. (2) Evaluate the integral -t t-2+i(t-1) i(3 - t) - 2y + iy²) dz. (3) Can the result of (2) be used to conclude that the function f(z) = x³ - 2y + iy² is not analytic at some point inside or on the contour T? Explain your answer carefully.
Let T be the contour given by the following parameterisation if 0 ≤ t ≤ 1 if 1 ≤ t ≤2 if 2 ≤ t ≤ 3. z(t) = x(t) + iy(t) = = (1) Sketch the contour T. (2) Evaluate the integral -t t-2+i(t-1) i(3 - t) - 2y + iy²) dz. (3) Can the result of (2) be used to conclude that the function f(z) = x³ - 2y + iy² is not analytic at some point inside or on the contour T? Explain your answer carefully.
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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![Let T be the contour given by the following parameterisation
if 0 ≤ t ≤ 1
if 1 ≤ t ≤ 2
if 2 ≤ t ≤ 3.
z(t) = x(t) + iy(t)
(1) Sketch the contour T.
(2) Evaluate the integral
E
-t
t - 2 + i(t-1)
i(3-t)
- 2y + iy²)dz.
(3) Can the result of (2) be used to conclude that the function f(z) = x³ – 2y + iy² is not
analytic at some point inside or on the contour T? Explain your answer carefully.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a7d82e4-2bf5-4850-ba06-9621bb0bd1d8%2F9874863c-85bb-4897-99f0-fbb4c76e917d%2Fcab4zbb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let T be the contour given by the following parameterisation
if 0 ≤ t ≤ 1
if 1 ≤ t ≤ 2
if 2 ≤ t ≤ 3.
z(t) = x(t) + iy(t)
(1) Sketch the contour T.
(2) Evaluate the integral
E
-t
t - 2 + i(t-1)
i(3-t)
- 2y + iy²)dz.
(3) Can the result of (2) be used to conclude that the function f(z) = x³ – 2y + iy² is not
analytic at some point inside or on the contour T? Explain your answer carefully.
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