# finding the conformal mapping and plotting complex conformal mapping in Matlab?

Discussion in 'MATLAB' started by Mike, Aug 29, 2006.

1. ### MikeGuest

Greetings everybody,

I am wondering if there is a way to find out the resultant curve for
the following conformal mapping:

w= (1-i *z) / (1- i * x * z)

where z is on the horizontal line a*i -infinity to a*i + infinity, and
"i" is the imaginary unit, "x" is a parameter.

I am guessing that this curve must be a circle, but I want to locate

Also it would be very helpful to visualize the conformal mapping in
Matlab. Any command for that?

Thanks

Mike, Aug 29, 2006

2. ### Robert IsraelGuest

Good guess. A fractional linear transformation such as this one
maps (straight lines and circles) to (straight lines and circles).
Since a straight line or circle is determined by three points on it,
all you have to do now is substitute three values for z. I might
suggest z=0 and z=infinity as two of the values. You could also
use the fact that (assuming a and x are real) your curve must be
symmetric about the real axis, because changing z from t+ia to
-t+ia takes w to its complex conjugate.

Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

Robert Israel, Aug 29, 2006

3. ### MikeGuest

Yes, but how to obtain the center and the radius?

Mike, Aug 29, 2006
4. ### Robert IsraelGuest

Did you try following my hint? What points did you get?

Robert Israel
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

Robert Israel, Aug 29, 2006
5. ### MikeGuest

I've found the circle using your hint that the curve must be symmetric
about the real axis. thanks a lot Robert! You are smart.

Mike, Aug 29, 2006