The third applet demonstrates the Argument Principle.

• Enter the coefficients of a polynomial (up to degree 4) in the form a+bi in the places on the bottom panel.
• Enter a radius in the top box on the right and press 'Apply'. The applet will plot the image of a circle, centre 0 with the entered radius, under the given polynomial.
• Change the radius, press 'Clear' and 'Apply' again.
• Try the polynomial z³-z² with a circle of radius 2. You should get the curve used on the cover of the Block C units!
• If you wish to see an animated change of radius enter two radii in the top two boxes on the right and press 'Animate'. Have fun!

First applet
Second applet