       Re: Sqrt of complex number

• To: mathgroup at smc.vnet.net
• Subject: [mg126672] Re: Sqrt of complex number
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Wed, 30 May 2012 04:10:44 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201205270842.EAA17817@smc.vnet.net> <jpvfh3\$q6g\$1@smc.vnet.net> <jq25u1\$6gl\$1@smc.vnet.net>

```On 5/29/2012 2:46 AM, David Bailey wrote:
.....
>>
>
> In addition to what others have said, it is maybe worth pointing out
> that in general, the Sqrt expression would be embedded in a larger
> expression, such as a+Sqrt[3-4 I]+42 - so what should Mathematica do? If
> it returns a list of all possible answers, that might not be acceptable
> to something that was expecting a single value,
That suggests to me that whatever was expecting a single value has a bug
in it.  Ideally if the mathematics dictates "there are multiple answers"
then a good program should be able to deal with it. Otherwise it is
not doing mathematics.

and anyway, expressions
> such as ArcSin[.2] would have an infinite number of answers!
There are several possible notations for infinite sets.
Here's one:  Table[f[x],x,1, Inf]

>
> The only possible alternative strategy would be not to evaluate at all,
No, see above.

> as is the case with Sqrt[x^2] (since the answer can by x or -x).
Root[x^2,n] works for me, if n is an integer.  We could have all even
n choose one sign and odd n choose the other.

These suggestions may not fit into today's Mathematica very well, but that
does not mean that a better system could not be constructed.

RJF

>
> David Bailey
> http://www.dbaileyconsultancy.co.uk
>
>

```

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