Comparison of sums of conjugates of Complex Numbers

      by Arran Sadlier

How to use the applet

Type in the real and imaginary parts of two complex numbers(z1 and z2) in the text boxes as shown in the applet. Then press the "Display inputs" button to display z1, z2, z1+z2, z1-z2, the conjugate of z1+z2 and the conjugate of z1-z2 on the graph. Press the "show addition" and "show subtraction" buttons to display the answers in the respective text boxes.

For a guided example on understanding the maths, simply first click on the 'start example' button. To continue press the 'next step in example' button. For the option of viewing the example again press the 'reset' button.

You can hide/show the addition results or the subtraction results by clicking the appropriate checkboxes.

Note: The input numbers are rounded off to integers, if they contain decimal parts, when used in the calculations for answers to z1+z2, z1-z2 and their conjugates. It is advisable to only input integer values for precision and clarity. It is also advisable to input values between -10 and +10 for clarity on the graph (as the Leaving Cert Course does not appear to deal with Complex Numbers whose values have decimal parts, or whose values are large).

GOOD LUCK!!

The Maths involved.

The main concept to be understood is that of the following two equations:

/z1 + /z2 = /(z1 + z2)

/z1 - /z2 = /(z1 - z2)