sqrt question

04072017, 11:34 PM
(This post was last modified: 04072017 11:38 PM by nsg.)
Post: #13




RE: sqrt question
(04072017 09:15 PM)Claudio L. Wrote: Assuming clear and consistent conventions (like always choosing the positive root for sqrt(), even if complex), You cannot do this because there is no such thing as "negative" for complex numbers. "Greater than" and "less then" are only defined for reals (number line). So, if you stay in real land, then sqrt(9)*sqrt(4) is undefined and if you expand into complex plane then it is +6. Square root in complex plane IS a multivalued function, there is simply no way around it. On a somewhat related note, i and i are algebraically indistinguishable. C is extension field of R, extended by roots of irreducible polynomial x^2+1=0. It is second degree polynomial, has 2 roots, we pick one of them arbitrarily, call it "i" and continue. We might as well could have picked another one (it is equal to i in our newly established convention) and have called THAT one "i" and would not notice any difference. This contrasts with 1 and 1, which are clearly algebraically distinct and whole bunch of equations will break if we replace 1 with 1 and 1 with 1. 

« Next Oldest  Next Newest »

Messages In This Thread 
sqrt question  KeithB  04062017, 03:25 PM
RE: sqrt question  pier4r  04062017, 04:01 PM
RE: sqrt question  Namir  04062017, 04:02 PM
RE: sqrt question  KeithB  04062017, 04:51 PM
RE: sqrt question  Han  04062017, 05:46 PM
RE: sqrt question  pier4r  04062017, 05:15 PM
RE: sqrt question  KeithB  04062017, 06:03 PM
RE: sqrt question  Han  04062017, 06:18 PM
RE: sqrt question  Claudio L.  04072017, 01:23 PM
RE: sqrt question  Han  04072017, 04:48 PM
RE: sqrt question  Claudio L.  04072017, 09:15 PM
RE: sqrt question  Han  04072017, 10:54 PM
RE: sqrt question  Claudio L.  04092017, 03:59 AM
RE: sqrt question  David Hayden  04242017, 09:36 PM
RE: sqrt question  Claudio L.  04262017, 03:08 AM
RE: sqrt question  Han  04282017, 06:09 PM
RE: sqrt question  nsg  04072017 11:34 PM
RE: sqrt question  Vtile  04092017, 10:41 AM
RE: sqrt question  nsg  04092017, 05:26 PM
RE: sqrt question  Vtile  04092017, 11:07 PM
RE: sqrt question  nsg  04102017, 01:44 AM
RE: sqrt question  Vtile  04252017, 11:38 PM

User(s) browsing this thread: 1 Guest(s)