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#8. If fiz) is analytic in a domain D and f(0) = 0, find fiz) so that Ref(z) = − x² + y² + 2xy - 2x.

#8. If fiz) is analytic in a domain D and f(0) = 0, find fiz) so that Ref(z) = − x² + y² + 2xy - 2x.

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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Please solve number 8
12:28: Back Homework Two.pdf #1. Let (a) lim 20 #2. Let f(2)= Homework Two 32+1 T(z) = show that Z-2 (b) lim T(z) = ∞0. 22 when 20 when z=0 (2) = 3 Does f'(o) exist? why?. #3. Define the operator 3/2/2 = = = = (2x + ²y). Show that fle)=u+iv satisfies Cauchy-Riemann equations if and only if It af € [² 0 #4. Let fiz)=√re², z=reid, r>o, o< 0 <2πi. Show that fiz) is analytic in the region, and find f'(z). #5. Let fiz) = find all singular points of fiz). z³³ + 8 2²-1 #6. Let fiz) be analytic in a domain D. Prove that fiz) must be constant through out D if I f(z) is constant in D. Dashboard #7. Show that if fiz) is analytic in some domain D which is symmetric about pure imaginary axis (yaxis) and f(z) is real on the imaginary axis, then f(z) = f(-2). #8. If fiz) is analytic in a domain D and f(0) = 0, find fiz) so that Ref(z) = _ x² + y² + 2xy - 2x. |88|1 Calendar 89 To Do C Notifications Inbox
Transcribed Image Text:12:28: Back Homework Two.pdf #1. Let (a) lim 20 #2. Let f(2)= Homework Two 32+1 T(z) = show that Z-2 (b) lim T(z) = ∞0. 22 when 20 when z=0 (2) = 3 Does f'(o) exist? why?. #3. Define the operator 3/2/2 = = = = (2x + ²y). Show that fle)=u+iv satisfies Cauchy-Riemann equations if and only if It af € [² 0 #4. Let fiz)=√re², z=reid, r>o, o< 0 <2πi. Show that fiz) is analytic in the region, and find f'(z). #5. Let fiz) = find all singular points of fiz). z³³ + 8 2²-1 #6. Let fiz) be analytic in a domain D. Prove that fiz) must be constant through out D if I f(z) is constant in D. Dashboard #7. Show that if fiz) is analytic in some domain D which is symmetric about pure imaginary axis (yaxis) and f(z) is real on the imaginary axis, then f(z) = f(-2). #8. If fiz) is analytic in a domain D and f(0) = 0, find fiz) so that Ref(z) = _ x² + y² + 2xy - 2x. |88|1 Calendar 89 To Do C Notifications Inbox
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