Re: Re: (-1)^(1/2.) on Mathematica!

• To: mathgroup at smc.vnet.net
• Subject: [mg107566] Re: [mg107548] Re: (-1)^(1/2.) on Mathematica!
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Wed, 17 Feb 2010 07:03:15 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <hlb8qi\$rm5\$1@smc.vnet.net> <201002160855.DAA01502@smc.vnet.net>

```No, (-1)^(1/2) does not have "two solutions".  The equation z^2 = -1 has
two solutions:

z /. Solve[z^2 == -1,z] // InputForm
{-I, I}

However, here you obtain just a single number as result:

(-1)^(1/2)  // InputForm
I

Similarly, the following gives just one single number as result ---

(-1)^(1/3) // ComplexExpand // InputForm
1/2 + (I/2)*Sqrt[3]

--- whereas:

z /. Solve[z^3 == -1, z] // ComplexExpand // InputForm
{-1, 1/2 + (I/2)*Sqrt[3], 1/2 - (I/2)*Sqrt[3]}

As the Documentation Center reference page for Power explains:
"For complex numbers x and y, Power gives the principal value of e^(y
log (x))."

On 2/16/2010 3:55 AM, ben wrote:
> Hi,
>
> It's fine on Mathematica 6.0, maybe the trouble is that
> (-1)^(1/2) has two solutions: "I" and "-I".
>
> Ben
>
> On Feb 15, 12:48 pm, Legendre<sinankap... at gmail.com>  wrote:
>> Hi,
>>
>> I tried the expression (-1)^(1/2.) on Mathematica 7.0, I got 6.12323*10^(-17) + 1. i. By using //N there is no problem. But using 2. it gives a wrong answer.
>>
>> Sinan
>
>

--
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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