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Problem 8. Let f(z) = u(x, y) iv(x, y) be an entire function with real and...

Question:

Problem 8. Let f(z) = u(x, y) iv(x, y) be an entire function with real and imaginary parts u(x, y) and v(x, y). Assume that t

Problem 8. Let f(z) = u(x, y) iv(x, y) be an entire function with real and imaginary parts u(x, y) and v(x, y). Assume that the imaginary part is bounded v(x, y) < M for every z = x+ iy. Prove that f is a constant 1

Answers

Liouvilles Theorem antire function Whieh is bounded, 1f fis an So that, 1f C2) M or Some M and for all 2 in C be ernstant thSinee, (2)is antire and bounded function in r an then, b1 Liouvilles theorem, a cmstant funchion 2)20 for some (1- 20 -if L

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