Re: Sqrt of complex number

*To*: mathgroup at smc.vnet.net*Subject*: [mg126647] Re: Sqrt of complex number*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Mon, 28 May 2012 05:12:23 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201205270842.EAA17817@smc.vnet.net>*Reply-to*: murray at math.umass.edu

As the documentation says: Sqrt[z] means z^(1/2) z^p gives the _principal value_ -- of Exp[p Log[z]]. As with any rational power 1/m, then, you'll need another way to find other roots. One way: z /. Solve[z^2 == 3 - 4 I, z] {-2 + I, 2 - I} (In some such situations, you'll want to wrap the z/.Solve[...] expression with ComplexExpand in order to get the Cartesian forms of the roots. On 5/27/12 4:42 AM, Jacare Omoplata 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. > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

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