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#1 2015-05-07 20:09:04

Olinguito
Member
Registered: 2014-08-12
Posts: 648

Principal roots




If z is real and positive, the principal root lies on the positive real axis and so is real.

If z is real and negative, the real root (if any) will not be on the positive real axis but there will still be a complex root in the first quadrant; the principal root in this case is complex.

This, at any rate, is Wolfram's definition; Wikipedia has a slightly different definition.





Last edited by Olinguito (2015-05-07 20:29:35)


Bassaricyon neblina

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#2 2015-05-08 00:17:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,105

Re: Principal roots

Hi Olinguito;

Mathematica, the engine behind Wolfram also exhibits this behavior. For instance to follow bob bundy's example given in the other thread if we enter

we get

which is complex, instead of the desired result of 0. Entering

also yields

To get the answer of 0 which is the result Olinguito and Bob expect, we enter

this returns 0 which is as it should be.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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