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Re: Sqrt of complex number

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  • Subject: [mg126638] Re: Sqrt of complex number
  • From: Bob Hanlon <hanlonr357 at>
  • Date: Mon, 28 May 2012 05:09:16 -0400 (EDT)
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  • References: <>

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

y /. Solve[y^2 == x, y]

{-Sqrt[x], Sqrt[x]}

y /. Solve[y^2 == 3 - 4 I, y]

{-2 + I, 2 - I}


Bob Hanlon

On Sun, May 27, 2012 at 4:42 AM, Jacare Omoplata
<walkeystalkey at> 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.

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