- #1
sgcbell2
- 3
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Hi, I am currently working on problem to do with conformal mappings and Mobius Transformations.
My problem is:
Find the Mobius Transformation which carries the points 1, i, 0 to the points ∞, 0, 1 (in precisely this order). Find the image of the domain { z : 0 < x < t} under this Mobius Transformation, where t > 0 is some fixed positive real number.
I have found this Mobius transformation to be (z-i)/i(z-1).
I thought that in order to find the image of the domain given above, I should input different values along the boundaries x=0 and x=t into this mobius transformations to see where they are mapped to. I have done this but I'm finding it hard to see the shape of the image.
Maybe I am doing something wrong?
My problem is:
Find the Mobius Transformation which carries the points 1, i, 0 to the points ∞, 0, 1 (in precisely this order). Find the image of the domain { z : 0 < x < t} under this Mobius Transformation, where t > 0 is some fixed positive real number.
I have found this Mobius transformation to be (z-i)/i(z-1).
I thought that in order to find the image of the domain given above, I should input different values along the boundaries x=0 and x=t into this mobius transformations to see where they are mapped to. I have done this but I'm finding it hard to see the shape of the image.
Maybe I am doing something wrong?