Math Mavens - Hopefully Easy Algebra Query

[Orbifold]

*Originally posted by DaveW *
**r[sub]1[/sub] = -(|m|[sup]1/3[/sup])
r[sub]2[/sub] = -(r[sub]1[/sub]/2) + (3[sup]1/2[/sup]/2)r[sub]1[/sub]i
r[sub]3[/sub] = -(r[sub]1[/sub]/2) - (3[sup]1/2[/sup]/2)r[sub]1[/sub]i

Are those right?
**

Yes.

**
If we swap all the signs, do we get cube roots for positive m?
**

Also yes.

[DaveW]

Cool! Thanks.

Actually, should all the signs be swapped for positive m, or just the sign of r[sub]1[/sub]?

[Cabbage]

DaveW

The nth roots of unity (1) are always very symmetrical, and can be found using trig functions. They are of the form:

cos(2kpi/n) + i sin(2kpi/n)

where k is an integer.

http://mathworld.wolfram.com/RootofUnity.html

[Cabbage]

Oh, and just switch the sign for r1. Switching all of the signs you have there looks like it will pretty much just get you back to what you started with.