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Re: Sqrt of complex number

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  • Subject: [mg126652] Re: Sqrt of complex number
  • From: David Bailey <dave at>
  • Date: Tue, 29 May 2012 05:45:27 -0400 (EDT)
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  • References: <> <jpvfh3$q6g$>

> 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

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