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Re: Sqrt of complex number

• To: mathgroup at smc.vnet.net
• Subject: [mg126643] Re: Sqrt of complex number
• From: Helen Read <readhpr at gmail.com>
• Date: Mon, 28 May 2012 05:11:00 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jpspgr$hdj$1@smc.vnet.net>

If you ask for the square root, cube root, or 4th root etc., Mathematica 
will return the principal root. To get them all, use Solve.

Solve[z^2 == 3 - 4 I, z]


Solve[z^3 == -8, z]

Solve[z^3 == -8, z] // ComplexExpand

Helen Read
University of Vermont


On 5/27/2012 4:44 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.
>