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Post by Admin on Feb 16, 2016 17:00:32 GMT
I have just published exercise 27 of chapter 5.
Vasco
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Post by Admin on Feb 18, 2016 16:43:56 GMT
Just corrected a typo in part (i). I had used angle $\phi$ throughout part (i) when it should have been $\sigma$.
Vasco
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Post by telemeter on Mar 3, 2019 18:47:20 GMT
Alternate approach I found interesting in the spirit of the transformations earlier in the book,
a) Move the relevant line/ circle to the origin: z maps to z-X and z-p for parts i) and ii) respectively
b) Conduct the "conjugation" operation: for i) rotate by -2 sigma to get (z-X)e-i2sigma and
ii) use our knowledge about reflection in a circle, z*= r2/ z to get r2/(z-p)
c) Move the result to the conjugate of the starting point : i) add X to get X+ (z-X)e-i2sigma which rearranges simply to get the book result
ii) add p* to get p* + r2/(z-p)
(using * as conjugate sign)
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