Does maximum modulus principle apply to an infinite strip?

[romiet3625]

[SOLVED] complex analysis - maximum modulus & analytic function

Hi all, I'm having difficulty figuring out how to do the following two problems in complex analysis. I need help!

1. Consider the infinite strip -$$\pi$$< I am z < $$\pi$$. Does maximum modulus principle apply to this strip? Why or why not? (Hint: e$$^{i\pi}$$ = e$$^{-i\pi}$$ = 1)



2. Show that if f(z) is analytic and Re f(z) is bounded in the complex plane, then f(z) is constant. What if I am f(z) is bounded? (Hint: Consider e$$^{f(z)}$$ and its absolute value)

Thank you for your time and thank you for any help.

 

[HallsofIvy]

You are given hints and you haven't used them? What have YOU done on this? No one can help you if you don't show us what YOU know about these problems and where you are having difficulties.