Evaluate (y - x - 3ix²) dz, where C' is the contour joining 0 and 1 + i in the following manners: (a) C is the straight line from 0 to 1 + i. (b) C is the straight line from 0 to i and then the straight line from i to 1+i. (c) C is the parabola y = r². 2² dz, where C'is the contour joining 0 and 1+i in the following Evaluate manners: (a) C is the straight line from 0 to 1 + i. (b) C is the straight line from 0 to i and then the straight line from i to 1 + i. (c) C is the parabola y = 1². 23 ·1+i dz Evaluate *** 2² dz using the formula [²²α = ²3²₁ What is your observation from the answers to questions 1, 2 and 3? From this observation, can you directly argue why 2² dz should be 0 for any closed contour C? Can you find any function other than f(z) = z² that can produce the same result? What kind of functions produce such result?

Evaluate (y - x - 3ix²) dz, where C' is the contour joining 0 and 1 + i in the following manners: (a) C is the straight line from 0 to 1 + i. (b) C is the straight line from 0 to i and then the straight line from i to 1+i. (c) C is the parabola y = r². 2² dz, where C'is the contour joining 0 and 1+i in the following Evaluate manners: (a) C is the straight line from 0 to 1 + i. (b) C is the straight line from 0 to i and then the straight line from i to 1 + i. (c) C is the parabola y = 1². 23 ·1+i dz Evaluate *** 2² dz using the formula [²²α = ²3²₁ What is your observation from the answers to questions 1, 2 and 3? From this observation, can you directly argue why 2² dz should be 0 for any closed contour C? Can you find any function other than f(z) = z² that can produce the same result? What kind of functions produce such result?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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