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1.1 Let u(x, y) = 4(x² – y²) – 5y. If f(x, y) = u(x, y) + iv(x, y) is an entire function, then v(x, y) = А. —8ху — 5х В. 8гу — 5х. C. 4y? + 5x +1. D. 8ry + 5x -12е. E. None of the above.

1.1 Let u(x, y) = 4(x² – y²) – 5y. If f(x, y) = u(x, y) + iv(x, y) is an entire function, then v(x, y) = А. —8ху — 5х В. 8гу — 5х. C. 4y? + 5x +1. D. 8ry + 5x -12е. E. None of the above.

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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1.1 Let u(x, y) = 4(x² – y²) – 5y. If f(x, y) = u(x, y) + iv(x, y) is an entire function, then v(x, y) = А. —8гу — 5х В. 8лу — 5х. С. 4у? + 5х + 1. D. 8ry + 5x —12е. E. None of the above. 1.2 Suppose f(2) = (z – i)³e² is analytic inside and on circle |z – i| = 3. Then the upper bound of |f(3) (i)| is А. без. 16e³ В. 27 С. бт. D. 16e3 9 E. None of the above. 1.3 If |f(2)| < M < o for all z € C. If it is further given that f is an entire function, which of the following best describe the given function f(2)? А. т — 2. B. e-iz. C. sin 2z. D. 23 – 5iz? – 5+ i. E. Not enough information.
Transcribed Image Text:1.1 Let u(x, y) = 4(x² – y²) – 5y. If f(x, y) = u(x, y) + iv(x, y) is an entire function, then v(x, y) = А. —8гу — 5х В. 8лу — 5х. С. 4у? + 5х + 1. D. 8ry + 5x —12е. E. None of the above. 1.2 Suppose f(2) = (z – i)³e² is analytic inside and on circle |z – i| = 3. Then the upper bound of |f(3) (i)| is А. без. 16e³ В. 27 С. бт. D. 16e3 9 E. None of the above. 1.3 If |f(2)| < M < o for all z € C. If it is further given that f is an entire function, which of the following best describe the given function f(2)? А. т — 2. B. e-iz. C. sin 2z. D. 23 – 5iz? – 5+ i. E. Not enough information.
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