Re: Having trouble with 92...
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> "Harry Elam" <hbe@way.com> writes:
> > "Xavier Scott" <joe@microsoft.com> writes:
> > When I put in (-27)^(1/3) and press enter, I get the following
> > answer:
> >
> > 3/2+3*sqrt(3)/2*i.
> >
> > What's with that? I know the answer is supposed to be -3. Can anyone
tell
> > me whay it is doing this?
> >
> >
> > Concerned Calculus Student-> Scott Johnson
> >>>>
> I don't have a TI-92, and my TI-83 doesn't behave like that, but all
negative
> numbers actually have three complex cube roots with the same absolute
> value and arguments pi/3, 2*pi/3, and pi. In the case of -27, they are:
>
> 3/2+3*sqrt(3)/2*i, -3/2+3*sqrt(3)/2*i, and -3
>
> I suggest you try changing the mode setting to Real, or something like that.
>
> Harry
>>>>
Sorry! What was I thinking? It's too early in the morning for this!
The arguments of the three roots are pi/3, -pi/3 (or 5*pi/3), and pi! In the
case
of 27, this gives:
3/2+3*sqrt(3)/2*i, 3/2-3*sqrt(3)/2*i, and -3
The complex roots are conjugates of each other.
Harry
References: