# [R] cube root of a negative number

Bill.Venables at csiro.au Bill.Venables at csiro.au
Wed Oct 27 01:34:27 CEST 2010

```To take it one step further:

> x <- as.complex(-4)
> cx <- x^(1/3)
>
> r <- complex(modulus = Mod(cx), argument = Arg(cx)*c(1,3,5))
> r
[1]  0.793701+1.37473i -1.587401+0.00000i  0.793701-1.37473i
> r^3
[1] -4+0i -4+0i -4+0i
>

So when you ask for "the" cube root of -4, R has a choice of three possible answers it can give you.

It is no surprise that this does not work when working in the real domain, except "by fluke" with something like

> -4^(1/3)
[1] -1.587401
>

where the precedence of the operators is not what you might expect.  Now that could be considered a bug, since apparently

> -4^(1/2)
[1] -2

which comes as rather a surprise!

Bill.

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Kjetil Halvorsen
Sent: Wednesday, 27 October 2010 9:17 AM
To: Gregory Ryslik
Cc: r-help Help
Subject: Re: [R] cube root of a negative number

Look at this:

> x <- as.complex(-4)
> x
[1] -4+0i
> x^(1/3)
[1] 0.793701+1.37473i
> (-4)^(1/3)
[1] NaN

It seems that R gives you the principal root, which is complex, and
not the real root.

Kjetil

On Tue, Oct 26, 2010 at 8:05 PM, Gregory Ryslik <rsaber at comcast.net> wrote:
> Hi,
>
> This might be me missing something painfully obvious but why does the cube root of the following produce an NaN?
>
>> (-4)^(1/3)
> [1] NaN
>>
>
> As we can see:
>
>> (-1.587401)^3
> [1] -4
>
> Thanks!
>
> Greg
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help