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>