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Re: Sqrt of complex number

• To: mathgroup at smc.vnet.net
• Subject: [mg126652] Re: Sqrt of complex number
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Tue, 29 May 2012 05:45:27 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201205270842.EAA17817@smc.vnet.net> <jpvfh3$q6g$1@smc.vnet.net>

>
> When I try to find the square root of of a complex number, I get only one
> answer.
>
> In[1]:= Sqrt[3-4 I]
> Out[1]= 2-I
>
> But -2+I is an answer as well.
>
> In[2]:= (-2+I)^2
> Out[2]= 3-4 I
>

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, and anyway, expressions 
such as ArcSin[.2] would have an infinite number of answers!

The only possible alternative strategy would be not to evaluate at all, 
as is the case with Sqrt[x^2] (since the answer can by x or -x).

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

• References:
  • Sqrt of complex number
    • From: Jacare Omoplata <walkeystalkey@gmail.com>