sqrt question

[Vtile]

(04-09-2017 05:26 PM)nsg Wrote:  

(04-09-2017 10:41 AM)Vtile Wrote:  Not partially true. In example in electrical engineering the -i and +i ( or -j & +j in reality ) do have a big difference.

I did not mean that i and -i are the same. Clearly, -i and +i are different numbers, what I tried to say is you just cannot meaningfully tell which one is which. We can fix one of them and call that one i and another -i, but we could also have picked another one and call THAT one i and the original -i and it would make no difference. You cannot do this with 1 and -1. If you call -1 "1" (this also turns 1 into "-1"), then all hell breaks loose.

If, on the other hand, you have example of some i/-i asymmetry, please bring it on.

If you make substitution 1=-1 that would mean that whole number line is substituted so 2 turns to -2 and so forth. With only means that the calculus is also mirrored.
How the calculus would go idk (I assume 1*1=-1 and -1*1=1 etc.) at this time of night I need to draw a picture in the morning with fresh eyes. What I mean with this is that isn't there a symmetry even there. Not as obvious direction change as in i+- case, but still. That said I'm not too deep in tjeory and might just make fool at myself here.