Posts: 167

Threads: 13

Joined: Sep 2008

No, it's an ambiguity in the square root function. The square root function is double-valued (if x^2=c, then (-x)^2=c as well) and it isn't possible to make it single-valued over the whole complex plane without having a discontinuity somewhere. This type of discontinuity is called a branch cut. From memory, the HP-50g makes the standard choice of having the cut along the negative real axis. So you'll find that it gives sqrt (-1) = i , sqrt (-1 + 0.000001 i) = i (roughly) but sqrt (-1 - 0.0000001 i) = -i (roughly).

This discontinuity means that equations like sqrt(ab) = sqrt(a) sqrt(b) are not necessarily true (e.g., try this with a = b = -1 + i on your HP-50g) and will sometimes not work. It's arguable that FACTOR on the HP-50g should be aware of the problem and refuse to do a rearrangement that might not work, but whether it works or not depends on the values of a and b which the calculator might not know.

Nigel (UK)