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Re: Different answers in mathematica and my calculator.
*To*: mathgroup at smc.vnet.net
*Subject*: [mg125598] Re: Different answers in mathematica and my calculator.
*From*: Murray Eisenberg <murray at math.umass.edu>
*Date*: Tue, 20 Mar 2012 02:24:23 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201203191000.FAA01033@smc.vnet.net>
*Reply-to*: murray at math.umass.edu
Everything boils down to what the value is of (-1)^(1/3), the cube-root
of -1.
The difference is because your calculator is brain-dead to complex
numbers! Mathematica, on the other hand, knows about complex numbers.
If you want to see the Cartesian form of that cube root, evaluate this:
ComplexExpand[(-1)^(1/3)]
The result, in input form, will be:
1/2 + (I/2)*Sqrt[3]
What Mathematica is giving you is the _principal_ cube-root of -1.
(This issue is one of the most frequently asked by Mathematica neophytes.)
On 3/19/12 6:00 AM, Nile wrote:
> 4/(3Power[2(-2)+3, (3)^-1])
>
> I get -(4/3) (-1)^(2/3) in Mathematica but only -4/3 on my calculator.
>
>
> N[Sec[8/(8 Sqrt[2])]]/Degree to get Cos^-1 of 8/(8 Sqrt[2]) and it gives me 75 deg instead of 45...
>
> I'm not sure what I'm doing wrong, I tried in Wolfram Alpha and it gives me the same thing.
>
> Thank you.
>
> -Francis
>
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
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