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7.14. Show that if f = u+iv is analytic in a region S and u is a constant function (i.e., independent of a and y), then f is a constant. 7.15. Show that if h : R2 → R and f = 2h3 + ih is an entire function, then h is a constant. %3D 7 1 SIOW . 7.17. Suppose that f = u + iv is analytic in a rectangle with sides parallel to the coordinate axes and satisfies the relation uz + 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. %3D

7.14. Show that if f = u+iv is analytic in a region S and u is a constant function (i.e., independent of a and y), then f is a constant. 7.15. Show that if h : R2 → R and f = 2h3 + ih is an entire function, then h is a constant. %3D 7 1 SIOW . 7.17. Suppose that f = u + iv is analytic in a rectangle with sides parallel to the coordinate axes and satisfies the relation uz + 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. %3D

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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7.14. Show that if f = u+iv is analytic in a region S and u is a constant function (i.e., independent ofx and y), thenf is a constant. 7.15. Show that if h : R2 → R and f = 2h3 + ih is an entire function, then h is a constant. %3D 7 1 SIOW . 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:7.14. Show that if f = u+iv is analytic in a region S and u is a constant function (i.e., independent ofx and y), thenf is a constant. 7.15. Show that if h : R2 → R and f = 2h3 + ih is an entire function, then h is a constant. %3D 7 1 SIOW . 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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