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 Exercise [08.04] 
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Joined: 12 Mar 2008, 10:57
Posts: 69
Location: India
Post Exercise [08.04]
The equation of a circle in z-plane is given by

z\overline{z}=kwhere k is a constant.

For taking any curve into w-plane we need to take every z in z-plane into w-plane using the given transformation.Thus,

z\rightarrow \frac{1}{z}and

\overline{z}\rightarrow\frac{1}{\overline{z}}

The given circle in the z-plane can also be represented as

\frac{1}{z\overline{z}}=\frac{1}{k}(z is not zero)

In the w-plane this amounts to,

w\overline{w}=\frac{1}{k}

which is again the equation of a circle.Hence,actual circles are mapped to actual circles by the reciprocal function.


13 Jul 2008, 14:36
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