Thread: complex analysis
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Old January 11th, 2009, 09:44 PM
manjohn12 manjohn12 is offline
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Default complex analysis
We know that there is only one linear fractional transformation that maps three given points z_1, z_2, z_3 to three specified points w_1, w_2, w_3. So the mapping \text{Im} \ z = 0 onto the circle |w| = 1 is uniquely determined if we choose the points (for example): z = 0, \ z = 1, \ z = \infty.



Why do we write w = e^{i \alpha} \frac{z-z_{0}}{z-z_{1}}. Where did the e^{i \alpha} come from?
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