The square root of any number x has two solutions: -sqrt(x) and +sqrt(x). This holds even for negative
numbers, where the solutions are in the complex number plane: -i sqrt(x) and +i sqrt(x). Therein,
i equals the square root of -1.
As a general law, the n-th root of a number x has n solutions...
Of course, it has much to do:
Leonhard Euler's four-squares identity prefigures quaternion multiplication:
It is the very reason why quaternions have a multiplicative norm, i.e. the length
of a product of two quaternions equals the product of the lengths of the
quaternions...
The 4-Squares-Identity of Leonhard Euler
(https://en.wikipedia.org/wiki/Euler%27s_four-square_identity) :
has the numeric structure of Maxwell’s equations in 4-space:
Is somebody aware of litterature about this?