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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

• References:
  • Different answers in mathematica and my calculator.
    • From: Nile <thrasher300@gmail.com>