Question

Can anybody help,
An entire function takes all its values on the imaginary axis. Prove that it is a constant
function.

Answer 1

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Answer 2

\[f(x) = (x^2 + x + 1)i\]
This function takes all its values on the imaginary axis, is it a constant function?

Answer 3

huaaa i dont know

Answer 4

I guess it is based on Liouville's theorem.. but the theorem is for every bounded entire function.
so..