[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
## Re: fractional powers

**From**: |
Marvin Vis |

**Subject**: |
Re: fractional powers |

**Date**: |
Tue, 12 Nov 96 11:53:37 MST |

>* I'm somewhat disturbed by the following behaviour on octave. Perhaps it*
>* is standard and I shouldn't be worried but it surprised me. Consider the*
>* following question: what is the cube root of -1? Clearly the answer*
>* should be -1. Now ask octave*
>* *
>* octave:1> x = (-1)^(1/3)*
>* x = 0.50000 + 0.86603i*
>* *
>* it gets wierder if you now cube that number*
>* *
>* octave:2> x^3*
>* ans = -1.0000e+00 + 1.2246e-16i*
>* *
>* This is pretty close to the truth but still strange to my way of thinking.*
>* Similar wierdness shows up with other fractional powers: 1/5, 1/7, etc.*
>* *
>* Any thoughts?*
There are actually 3 cube roots of -1 (here, j = sqrt(-1)):
(-1)^(1/3) = {exp(j*pi/3), exp(-j*pi/3), -1}
Most rooting algo's will find the n^th root of a number as follows:
Starting with a number z = |z|*exp(j*theta),
z^(1/n) = |z|^(1/n) * exp(j*theta/n)
I'd call this the primary root. If you want to have a special case for
negative (real) z and odd n, you could use a routine that does:
z^(1/n) = - |z|^(1/n)
This would give you -1 as the cube root of -1.
M.