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.