brian87
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Homework Statement
Suppose that f is entire and \lim_{z \to \infty}\frac{f(z)}{z} = 0. Prove that f is constant.
z, and f(z) are in the complex plane
The attempt at a solution
I've tried to find out how the condition \lim_{z \to \infty}\frac{f(z)}{z} = 0 implies the function itself is bounded, but I've not been successful in doing so.
Any hints?
Thanks :)
Suppose that f is entire and \lim_{z \to \infty}\frac{f(z)}{z} = 0. Prove that f is constant.
z, and f(z) are in the complex plane
The attempt at a solution
I've tried to find out how the condition \lim_{z \to \infty}\frac{f(z)}{z} = 0 implies the function itself is bounded, but I've not been successful in doing so.
Any hints?

Thanks :)
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