Re: Sqrt of complex number

• To: mathgroup at smc.vnet.net
• Subject: [mg126638] Re: Sqrt of complex number
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Mon, 28 May 2012 05:09:16 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201205270842.EAA17817@smc.vnet.net>

```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
are

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

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

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

{-2 + I, 2 - I}

See http://reference.wolfram.com/mathematica/tutorial/FunctionsThatDoNotHaveUniqueValues.html

Bob Hanlon

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