Find an analytic function f(z) where the real part u(x,y) = ... | Filo
Find an analytic function f(z) where the real part u(x,y) = ... | Filo
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Find the analytic function f(z) = u iv , if 2u v = e^x(\c... | Filo
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[GET ANSWER] find an analytic function whose real part is e xx sin y y cos y 32897
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20:49←VOLTE(i) Find the analytic function f(z) = u iv whos... | Filo
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SOLVED:Let a function f(z) be analytic in a domain D. Prove that f(z) must be constant throughout D if (a) f(z) is real-valued for all z in D; (b) |f(z)| is constant throughout D. Suggestion: Use the Cauchy-Riemann equations and the theorem in Sec. 23 to prove part (a) . To prove part (b), observe that f(z)=(c^2)/(f(z)) if |f(z)|=c(c ≠0) then use the main result in Example 3, Sec. 24 .
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