The aim of this web application is to use polynomial functions to illustrate the principle of the argument.
Two screens are displayed. The left is the domain and the right is the codomain.
The image, under the chosen polynomial, of the set on drawn on the left is displayed on the right.
The winding number of the image about zero corresponds to the number of roots inside the circle drawn in the domain.
- Choose a polynomial. You may do this by pressing either 'Choose roots'
or 'Choose coefficients'. A window will open
allowing you to make your choices. Enter complex numbers using 'i'. For example 2-i.
- Alternatively you can select up to 4 roots by clicking on the domain with the mouse.
- The set in the domain is a circle, centre 0.
- You can choose values of two radii. If the value of the second radius is greater
than the value of the first, pressing 'Plot' will show you an animated sequence with
the radius increasing from the first value to the second.
- Otherwise the domain set and image will be drawn, slowly, once using the first radius.
- Pressing 'Stop' stops the animation.
- Pressing 'Zoom in' and 'Zoom out' re-scales the codomain.
- Pressing 'Reset' clears the screen and resets the polynomial to 'z'.