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Re: Sqrt of complex number

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  • Subject: [mg126647] Re: Sqrt of complex number
  • From: Murray Eisenberg <murray at>
  • Date: Mon, 28 May 2012 05:12:23 -0400 (EDT)
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  • Reply-to: murray at

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 

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
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University of Massachusetts                413 545-2859 (W)
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Amherst, MA 01003-9305

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