sqrt question

04092017, 03:59 AM
(This post was last modified: 04092017 04:01 AM by Claudio L..)
Post: #14




RE: sqrt question
(04072017 10:54 PM)Han Wrote: 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. The factorization properties hold true for complex numbers. The problem is more about the interaction between the sqrt() function and its argument because of mapping to the principal branch. For example: sqrt(1) = 1 sqrt( (1)*(1) ) = sqrt(1)*sqrt(1) = i*i = 1 What happened here? we replaced 1 (in polar coordinates, its argument is zero), with two numbers with an argument of 180 degrees. The multiplication of these 2 numbers (1) would give you an argument of 360 degrees. The convention for sqrt is to halve the argument, so the result of sqrt(1*exp(i*2pi)) is 1*exp(i*pi) = 1 while sqrt(1*exp(i*0)) = 1*exp(i*0) = 1 Now the value 1*exp(i*2pi) should've been reduced to 1*exp(i*0) prior to performing the sqrt(). However, when you distribute the sqrt doing sqrt(1)*sqrt(1), you are not allowing that reduction to take place. Both arguments of 180 degree get halved, then added together by the multiplication resulting in 180 degree again (hence the negative result). So this is a consequence that 1 = (1)*(1), while mathematically true and correct, gets treated differently by the sqrt() when you split it. But there's nothing wrong, the result is correct, just that you've been pushed to the other solution. There's no way around it that I know of. 

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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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