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**[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 -[tex]\pi[/tex]< Im z < [tex]\pi[/tex]. Does maximum modulus principle apply to this strip? Why or why not? (Hint: e[tex]^{i\pi}[/tex] = e[tex]^{-i\pi}[/tex] = 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[tex]^{f(z)}[/tex] and its absolute value)**

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