The inversion studied in this sketch is the inversion with center O and inversion-circle the green circle.
You may drag the red point M. It's image in the inversion is the blue point M'.
In terms of complex numbers, if z is the affix of M, the affix of M' will be 1/conj(z),
that is the algebraic inverse of the complex conjugate of z.
Problems
1. For what positions of M do we have M' = M?
2. For fixed O and M,
is it possible to choose the point 1 so that M' = M?
In the following problems you should make use of the buttons.
3. If you move M along a vertical line, on what kind of curve does M' move?
4. Draw in the picture an approximative sketch of the set of points M such that M'
is on the square or outside it.
Draw a cleaner picture on the paper!