# Complex analysis - maximum modulus &amp; analytic function

[SOLVED] complex analysis - maximum modulus &amp; 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 -$$\pi$$< Im 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 Im f(z) is bounded? (Hint: Consider e$$^{f(z)}$$ and its absolute value)

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