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Find the image of the unit circle under the transformation, f(z) = 21 - and also find fixed points. Find the bilinear transformation which

Find the image of the unit circle under the transformation, f(z) = 21 - and also find fixed points. Find the bilinear transformation which maps the points 1,i,-1 onto the points 0,1,00 and show that this transformation maps the interior of the unit circle of the z-plane onto the upper half of the w-plane.

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