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**scorpio1** Unsure if this is the right section but here goes:

**By coordinte geometry, any line or circle is of the form Ax+By+C($\displaystyle x^2 + y^2$) = D, where A, B, C, D are real constants.**

**Set $\displaystyle \frac{1}{z}$ = u + iv.**

**Show that u = $\displaystyle \frac{x}{x^2 + y^2}$ and v = $\displaystyle \frac{-y}{x^2 + y^2}$.**

**Deduce that the linear fractional transformation sends a line or a circle to another such.**

I'm really quite stumped by this...I don't see where the 1/z comes into all this...and just in general don't know how to start with this?

Any hints or help would be greatly appreciated.