Re: Sqrt of complex number

*To*: mathgroup at smc.vnet.net*Subject*: [mg126645] Re: Sqrt of complex number*From*: Erik Max Francis <max at alcyone.com>*Date*: Mon, 28 May 2012 05:11:41 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jpspgr$hdj$1@smc.vnet.net>

On 05/27/2012 01:44 AM, Jacare Omoplata wrote: > 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? It's the principal square root. Does this result surprise you, after all, even though -2 squared is also 4? In[3]:= Sqrt[4] Out[3]= 2 If you want to actually ask for _all_ the possible answers, use Solve: In[1]:= Solve[x^2 == 3 - 4 I, x] Out[1]= {{x -> -2 + I}, {x -> 2 - I}} -- Erik Max Francis && max at alcyone.com && http://www.alcyone.com/max/ San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Jabber erikmaxfrancis The side that stays within its fortifications is beaten. -- Napoleon Bonaparte