Manipulate images with f(z)=1/conjugated(z)

I have to write a program in c++ or in any other language which manipulates images.

http://denesb.com/index.php/teac...
Here you can find an example, look only the pictures because the language is not english.

Description:
Input: picture, r(radius)
output: the new picture

We go the center of the image which we got from the user, then the user gives us a radius, so now we have a circle.

Then we have to throw out the pixels from the inner circle and we have to throw in the pixels from the outer circle with this function:
f(z)=1/conjugated(z) ------- z is a complex number

Any idea would help me a lot, thanks very much:)))
Use an image processing library for C++ - Google has plenty of good results.

For example, CImg:
http://cimg.eu/
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