Interesting Complex numbers problem

Algebra Level 5

A transformation T from the Z plane to the W plane is given by

\[ W = \frac{Z}{Z+i}, \quad Z\neq -i \]

The circle with equation \(|Z| = 3\) is mapped by T onto the Curve "C" which is also a circle.

Find the value of G/R where G is the x value of the coordinate of the center of the circle C and R is the radius of the circle C


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