Complex number arithmetic and geometry

This applet is to show the relationship between arithmetic of complex numbers and the corresponding geometry on an Argand diagram. Click and drag the points and . Check or uncheck the arithmetic operations in the right-panel. In particular pay attention to the following:
  • Addition and subtraction of complex numbers works like vector addition and subtraction in the plane.
  • Multiplication: the new complex number can be obtained by adding the arguments (angles) and multiplying the moduli (lengths).
  • Division: the new complex number can be obtained by subtracting the arguments (angles) and dividing the moduli (lengths).
The order of subtraction and division obviously matters so only and are shown to stop the app getting too crowded.