Maths - Inverse Of Double Numbers

To calculate the inverse value (1/z) we multiply the top and bottom by the conjugate which makes the denominator a real number.

z plane   w plane
z plane

-->

w=1/z

w invert

how this plot was produced.

Let the components of the input and output planes be:

z = x + D y and w = u + D v

In this case w = 1/z

so:

w = 1/(x + D y)

As usual, we evaluate the inverse by multiplying top and bottom by the conjugate:

w = (x - D y)/(x + D y)(x - D y)

w = (x - D y)/(x² - y²)

so the u and v components are:

u = x /(x²-y²)
v = -y /(x²-y²)

 


metadata block
see also:

 

Correspondence about this page Open Forum

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

coverus uk de jp fr ca Complex Numbers

cover Engineering Mathematics - This book has been going for a long time and it is now in its 5th edition, so it is tried and tested.

Terminology and Notation

Specific to this page here:

 

This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2023 Martin John Baker - All rights reserved - privacy policy.