I need a conformal mapping that would map an ellipse or a circle to a line. I need this for the third problem. As far as I can understand, z^2 + 1/z^2 makes the geometry similar to that of a plane on the horizontal axis with a circle centered on the origin. I can use the method of images (I think) but I was thinking of another map that would flatten out the circle and keep that plane in its current form. Not that it matters, I tried to tailor the homographic projection to my needs but couldn't get it to work.