Only recently I discovered that there is a class of complex numbers named hypercomplex numbers.(adsbygoogle = window.adsbygoogle || []).push({});

Hamilton invented (or discovered) the quaternions in 1843.

i² = j² = k² = ijk = -1

I understand how complex numbers work, but I don't understand how hypercomplex numbers work.

Can someone explain the following:

First, Hamilton tried to expand the two dimensional complex plane (Argand plane) to three dimensions. But he failed to work with tripleds.

Why?

for example, why does i² = j² = ij = -1 not work?

Second, how did he discover that in 4 dimensions he could work with entities called quaternions?

how did he invent i² = j² = k² = ijk = -1

ij = k

jk = i

ki = j

ji = -k

kj = -i

ik = -j

Third, can someone give me an example to work with quaternions? what can you do with them?

Dimsun

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Triplets and quaternions

**Physics Forums | Science Articles, Homework Help, Discussion**