Argument Principle Demo

Press the "Launch" button below to open the argument principle applet window:

Instructions: The complex plane is displayed. Use the mouse to add zeros and/or poles of a complex rational function f(z). z is specified by the position of the mouse, and f(z) is plotted by the coloured line. Encircle z about one or multiple zeros and/or poles, and observe the trajectory of f(z). Press 'D' to toggle pretty pictures. Command reference:

Command Description Left-click or "1" Adds zero. Right-click or "2" Adds pole. Middle-click or "3" Removes nearest zero or pole. C Clears all zeros and poles. N Normalize: Displays only the phase of f(z). D Toggles display mode: Single point view vs. phase plot view. P Changes colouring scheme. <Space> Selects phase offset (phase under mouse becomes 0). <Left>, <Right> Rotates phase offset. S Shrinks every zero and pole.

This program was written in April 2008, while I was a TA for ECE356S: Linear Systems and Control.