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#2. Define the operators 33/32 = 1/2 (3x +²y), 32= 2 (x-7) = u(x, y) +iv(x, y), show that (af (3) = ²/2 F. dž let f

#2. Define the operators 33/32 = 1/2 (3x +²y), 32= 2 (x-7) = u(x, y) +iv(x, y), show that (af (3) = ²/2 F. dž let f

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. ca) perform the operation (1-√32)-10 (6) Find the cubic roots of 1+√3 2. Express your answer in rectangular coordinates. #2. Define the operators 32/32 = 1/2 (124² +izy), 3 = 2 (x-7) ду, let f #5. = u(x, y) +iv(x, y), show that (3) #3. (a) If fiz) is analytic in a domain D and Ref = constant, Show that fizi = constant. (b) If f(z) is analytic in a domain I and Imf=x²-y² + 2xy, find flz). #4. (a) Let fiz) = Log (z +1) ~ Log (2-1), Find flz), fi-z), f(i). (b) let g(z) = ziti, find g(i). 14 = de f Sin z = 0 if and only if z=kπ, k=0, ±1, ±2.... (a) Show that (6) show that | Sinz | ² = sin³x + sinh ²y, z=xtiy. 2
Transcribed Image Text:#1. ca) perform the operation (1-√32)-10 (6) Find the cubic roots of 1+√3 2. Express your answer in rectangular coordinates. #2. Define the operators 32/32 = 1/2 (124² +izy), 3 = 2 (x-7) ду, let f #5. = u(x, y) +iv(x, y), show that (3) #3. (a) If fiz) is analytic in a domain D and Ref = constant, Show that fizi = constant. (b) If f(z) is analytic in a domain I and Imf=x²-y² + 2xy, find flz). #4. (a) Let fiz) = Log (z +1) ~ Log (2-1), Find flz), fi-z), f(i). (b) let g(z) = ziti, find g(i). 14 = de f Sin z = 0 if and only if z=kπ, k=0, ±1, ±2.... (a) Show that (6) show that | Sinz | ² = sin³x + sinh ²y, z=xtiy. 2
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