Re: Sqrt of complex number

*To*: mathgroup at smc.vnet.net*Subject*: [mg126638] Re: Sqrt of complex number*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Mon, 28 May 2012 05:09:16 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201205270842.EAA17817@smc.vnet.net>

A function (e.g., Sqrt) must be single-valued at each point so Sqrt is defined as the "principal root." The two values you are looking for are y /. Solve[y^2 == x, y] {-Sqrt[x], Sqrt[x]} y /. Solve[y^2 == 3 - 4 I, y] {-2 + I, 2 - I} See http://reference.wolfram.com/mathematica/tutorial/FunctionsThatDoNotHaveUniqueValues.html Bob Hanlon On Sun, May 27, 2012 at 4:42 AM, Jacare Omoplata <walkeystalkey at gmail.com> wrote: > Hi, > > 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 > > Why does Mathematica give the first answer and not the second? Does it choose the answer with the positive real number? Is there any way I can get both answers? Or do I just have to remember that the negative of the given answer is also an answer? > > Thanks. >

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