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**Homework Statement**

Suppose that f is entire and [tex]\lim_{z \to \infty}\frac{f(z)}{z} = 0[/tex]. 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 [tex]\lim_{z \to \infty}\frac{f(z)}{z} = 0[/tex] implies the function itself is bounded, but I've not been successful in doing so.

Any hints?

Thanks :)

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