The equation of a circle in z-plane is given by

where 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,

and

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

(z is not zero)

In the w-plane this amounts to,

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