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 Exercise [09.05] 
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Joined: 12 Mar 2008, 10:57
Posts: 69
Location: India
Post Exercise [09.05]
The given transformation is
z=\frac{-t+i}{t+i}
It can also be written as,
z=\frac{(-t+i)(t-i)}{(t+i)(t-i)}=\frac{1-t^2}{1+t^2}+i\frac{2t}{1+t^2}...(1)
The unit circle in the z-plane is characterised by the equation
|z|=1
Hence z can be written as follows,
z=\cos{\chi}+i\sin{\chi}=\frac{1-\tan^{2}{(\chi/2})}{1+\tan^{2}{(\chi/2)}}+i\frac{2\tan{(\chi/2)}}{1+\tan^{2}{(\chi/2)}}...(2)
Comparing (1)&(2)we get,
t=\tan{(\chi/2)}


23 May 2008, 11:43
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