Holomorphic 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

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.