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>
- Reply-to: murray at math.umass.edu
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
- References:
- Re: (-1)^(1/2.) on Mathematica!
- From: ben <benjamin.friedrich@gmail.com>
- Re: (-1)^(1/2.) on Mathematica!