Functions of a quaternion variable

Like functions of a circuitous variable, functions of a quaternion capricious advance advantageous concrete models. For example, the aboriginal electric and alluring fields declared by Maxwell were functions of a quaternion variable.

editExponential, logarithm, and power

Given a quaternion,

,

the exponential is computed as

and

.21

It follows that the arctic atomization of a quaternion may be written

where the bend and the assemblage agent are authentic by:

and

Any assemblage quaternion may be bidding in arctic anatomy as .

The ability of a quaternion aloft to an approximate (real) backer is accustomed by: