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Let C denote the line segment from the point -2+i to the point 1+7i and let f(2) where z = x + iy. Use the definition of a contour integral to calculate [ f(z) dz. branch of 1/4 much that lets O = x² + i(3y - x), ulon noth

Let C denote the line segment from the point -2+i to the point 1+7i and let f(2) where z = x + iy. Use the definition of a contour integral to calculate [ f(z) dz. branch of 1/4 much that lets O = x² + i(3y - x), ulon noth

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Questions: 1. Let C denote the line segment from the point −2+ i to the point 1+ 7i and let ƒ(z) where z = x + iy. Use the definition of a contour integral to calculate f(z) dz. = x² + i(3y − x), 2. Let ƒ be the branch of z¹/4 such that |z| > 0 and 0 < arg z < 2π. Let С denote the semi-circular path 2 = 2e²0 (0 ≤ 0 ≤ π).
Transcribed Image Text:Questions: 1. Let C denote the line segment from the point −2+ i to the point 1+ 7i and let ƒ(z) where z = x + iy. Use the definition of a contour integral to calculate f(z) dz. = x² + i(3y − x), 2. Let ƒ be the branch of z¹/4 such that |z| > 0 and 0 < arg z < 2π. Let С denote the semi-circular path 2 = 2e²0 (0 ≤ 0 ≤ π).
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