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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 -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
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.
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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