Complex Analysis-Entire Functions

[WannaBe22]

Homework Statement

Prove Or find a proper counterexample:
1. Let f be an entire function such as f(0)=101 and:
Re f(z) \geq 100 + Im(z) . Then f(i)=102 .

2. There exists an analytic function f from the unit circle to itself which satisfy:
f(\frac{i}{3})=\frac{1}{2} , f(\frac{1}{2}) = \frac{i}{3}.


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Homework Equations

The Attempt at a Solution

 

[Office_Shredder]

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