Question: Suppose f is entire function such that for some a, b > 0, If (2) | salz| + b for any & E C. Prove

Suppose f is entire function such that for some a, b

Suppose f is entire function such that for some a, b > 0, If (2) | salz| + b for any & E C. Prove that f is a linear function, i.e. f (z) = az + / for some a, B E C. (Hint: use the generalized Cauchy Integral formula to show that the f"(2) = 0 for all z e C.)

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