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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