# Re: Having trouble with 92...

```>   "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
>  >
>  >    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

```

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