Complex Analysis

  • #1
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Homework Statement


Find all analytic functions ƒ: ℂ→ℂ such that
|ƒ(z)-1| + |ƒ(z)+1| = 4 for all z∈ℂ and ƒ(0) = √3 i

The Attempt at a Solution


I see that the sum of the distance is constant hence it should represent an ellipse. However, I am not able to find the exact form for ƒ(z). Any help is appreciated. Thanks.
 

Answers and Replies

  • #2
Dick
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Homework Statement


Find all analytic functions ƒ: ℂ→ℂ such that
|ƒ(z)-1| + |ƒ(z)+1| = 4 for all z∈ℂ and ƒ(0) = √3 i

The Attempt at a Solution


I see that the sum of the distance is constant hence it should represent an ellipse. However, I am not able to find the exact form for ƒ(z). Any help is appreciated. Thanks.

Do you know Liouville's theorem?
 

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