+ iv is analyt: and satisfies the a real constant

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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7.17. Suppose that f = u + iv is analytic in a rectangle with sides
parallel to the coordinate axes and satisfies the relation u, + vy = 0 for all
x and y. Show that there exist a real constant c and a complex constant d
such that f(z) = -icz + d.
Transcribed Image Text:7.17. Suppose that f = u + iv is analytic in a rectangle with sides parallel to the coordinate axes and satisfies the relation u, + vy = 0 for all x and y. Show that there exist a real constant c and a complex constant d such that f(z) = -icz + d.
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