let f be an entire function..
1) prove if e^f is bounded then f is constant
2) prove that if Re f is bounded then f is constant
i'm guessing you would have to use suitable exponentials but i don't have a good enough idea of what to do here. any help would be greatly appreciated xx
also, if the result follows from louville's theorem, are we meant to show the taylor series for e^f about 0??? where would we go from there.. i would be greatful if you could show me what is to be done here???