From: Martin DeMello <martindemello@...>
Date: 2011-05-15T03:12:09+09:00
Subject: Re: Math cube root

On Fri, May 13, 2011 at 12:00 AM, Josh Cheek <josh.cheek@gmail.com> wrote:
> On Thu, May 12, 2011 at 10:26 AM, Colin Bartlett <colinb2r@googlemail.com>wrote:
>> which also changes this:
>>  (-1) ** (1.0 / 3) #=> NaN
>> to:
>>  (-1) ** (1.0 / 3) #=> (0.5+0.866025403784439i)
>> so we can also get complex roots if we want them!
>>
>>
> Which we don't here, given that the cube root of -1 isn't imaginary :/

Think of -1 in polar form (r exp(i theta)) as 1.exp(i pi), then note
that the cube roots are (1 exp (i pi/3)), (1 exp (i 2pi/3)) and (1
exp(i pi)). The principal cube root is the one with the smallest value
of theta.

martin