Associated Topics || Dr. Math Home || Search Dr. Math

### Inverse Quaternions

```
Date: 12/01/1999 at 06:09:16
From: Jarno Kuoppamaki
Subject: Inverse Quaternions

How do you calculate inverse quaternions? For example, the inverse of
3 - 4i + 5j + 6k.
```

```
Date: 12/01/1999 at 12:27:40
From: Doctor Rob
Subject: Re: Inverse Quaternions

Thanks for writing to Ask Dr. Math, Jarno.

Call a = 3 - 4*i + 5*j + 6*k. Write the inverse in the form 1/a.
Multiply the numerator and denominator by a with -i substituted for i,
-j substituted for j, and -k substituted for k, or

3 + 4*i - 5*j - 6*k

Expand and simplify the denominator, which should result in a real
number, 86 in this case:

86 = 3^2 + (-4)^2 + 5^2 + 6^2

Divide that real denominator into each coefficient in the numerator.
Result:

1/a = 3/86 + (4/86)*i - (5/86)*j - (6/86)*k

- Doctor Rob, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
College Modern Algebra

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search