sqrt question

04072017, 04:48 PM
(This post was last modified: 04072017 04:48 PM by Han.)
Post: #10




RE: sqrt question
(04072017 01:23 PM)Claudio L. Wrote: Both answers are correct! There are some nuances here that perhaps we are glossing over. Using the notation \( \sqrt{x} \) (which has a standard mathematical convention of meaning the positive root) to denote an extension into the complex plane means certain properties that were true only for nonnegative real values of \(x \) no longer hold for more general \( x \). Ordinary \( \sqrt{x} \) is a function, whereas complex \( \sqrt{x} \) is a 1to2 map (not a function). 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. Another question (regarding consistency) is why one would take \( \sqrt{4} \) to be 2i and \( \sqrt{9} \) to be 3i (i.e. one positive and the other negative, leading to inconsistency in the signs)? For functions, they should both be positive or both be negative. For more general maps, this is not a concern. Graph 3D  QPI  SolveSys 

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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

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