What are all entire holomorphic function for which is Re f(z)<=Im f(z)

for every z from C?

Hint: use Picard theorem

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- June 5th 2006, 03:24 AMnatyHolomorphic function
What are all entire holomorphic function for which is Re f(z)<=Im f(z)

for every z from C?

Hint: use Picard theorem - August 17th 2007, 03:01 AMRebesques
Since it is entire, we don't need to add "holomorphic". :)

Consider the function This is also entire and

, so the function is bounded. So it must be constant; That is, must be constant, or is constant. From this we get are constant.