# Thread: Mobius Transformations

1. ## Mobius Transformations

Unsure if this is the right section but here goes:

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

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

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

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.

2. Originally Posted by 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( $x^2 + y^2$) = D, where A, B, C, D are real constants.

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

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

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.
You are dealing with a circle (or line) in the complex plain, thus z=x+iy. now proceed.

RonL