sqrt question

[Han]

(04-07-2017 09:15 PM)Claudio L. Wrote:  

(04-07-2017 04:48 PM)Han Wrote:  So if we want the operation to behave as a function, there cannot be multiple answers. On the other hand, if this is not an issue, then both 6 and -6 are "correct" answers.

We visited this subject in the past (gave me a big headache!):

http://www.hpmuseum.org/forum/thread-6165.html

Assuming clear and consistent conventions (like always choosing the positive root for sqrt(), even if complex), the most trivial algebraic operations may switch you to the other branch (against your will):

sqrt(x) = sqrt((-1)*(-1)*x) = sqrt( -x*i^2) = i*sqrt(-x)

Not so equal!

Is this due to the sqrt() function, though? This seems like a consequence of assuming factorization properties of 1 and -1 that may not still hold true for complex numbers.