Re: nth roots of complex numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg39364] Re: nth roots of complex numbers
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 12 Feb 2003 03:54:11 -0500 (EST)
• Organization: The University of Western Australia
• References: <b10ddh\$mou\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <b10ddh\$mou\$1 at smc.vnet.net>,
"Zachary Turner" <_NOzturner0826SPAM_ at hotmail.com> wrote:

> Apparently Mathematica randomly returns roots a root of a complex number.
> Is there a way I can write my own function that will return a set consisting
> of all n roots of a given complex number.  For example, Root[z,n] = {a set
> consisting of n elements}

Actually Root is a built-in object -- and it can be used to do what you
want.

In[1]:= root[n_][z_] := Table[Root[#1^n - z & , k], {k, n}]

In[2]:= root[4][1]
Out[2]= {-1, 1, -I, I}

In[3]:= root[4][1 + I]
Out[3]= {Root[#1^8 - 2*#1^4 + 2 &, 1], Root[#1^8 - 2*#1^4 + 2 &, 4],
Root[#1^8 - 2*#1^4 + 2 &, 5],   Root[#1^8 - 2*#1^4 + 2 &, 8]}

In[4]:=N[%]
Out[4]={-1.0695539323639858 - 0.21274750472674303*I,
-0.21274750472674303 + 1.0695539323639858*I,
0.21274750472674303 - 1.0695539323639858*I,
1.0695539323639858 + 0.21274750472674303*I}

Cheers,
Paul

```

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