# Math Mavens - Hopefully Easy Algebra Query

**URL:** <https://boards.straightdope.com/t/math-mavens-hopefully-easy-algebra-query/162633>\
**Category:** Factual Questions\
**Created:** [March 19, 2003, 9:13pm UTC](https://boards.straightdope.com/t/math-mavens-hopefully-easy-algebra-query/162633 "2003-03-19T21:13:30Z")\
**Posts on this page:** 4\
**Page:** 3

<div class="post-metadata">

**Author:** ![Orbifold](https://avatars.discourse-cdn.com/v4/letter/o/779978/32.png) [@Orbifold](https://boards.straightdope.com/u/Orbifold)\
**Post date:** [March 21, 2003, 8:23pm UTC](https://boards.straightdope.com/t/math-mavens-hopefully-easy-algebra-query/162633/41 "2003-03-21T20:23:56Z")

</div>

> [@](#):
>
> \*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.

---

<div class="post-metadata">

**Author:** ![DaveW](https://avatars.discourse-cdn.com/v4/letter/d/9d8465/32.png) [@DaveW](https://boards.straightdope.com/u/DaveW)\
**Post date:** [March 21, 2003, 8:44pm UTC](https://boards.straightdope.com/t/math-mavens-hopefully-easy-algebra-query/162633/42 "2003-03-21T20:44:58Z")

</div>

Cool! Thanks.

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

---

<div class="post-metadata">

**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\
**Post date:** [March 21, 2003, 8:51pm UTC](https://boards.straightdope.com/t/math-mavens-hopefully-easy-algebra-query/162633/43 "2003-03-21T20:51:21Z")

</div>

**DaveW**

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

cos(2k **pi** /n) + i sin(2k **pi** /n)

where k is an integer.

[http://mathworld.wolfram.com/RootofUnity.html](http://mathworld.wolfram.com/RootofUnity.html)

---

<div class="post-metadata">

**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\
**Post date:** [March 21, 2003, 8:57pm UTC](https://boards.straightdope.com/t/math-mavens-hopefully-easy-algebra-query/162633/44 "2003-03-21T20:57:49Z")

</div>

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.

[Previous page](https://boards.straightdope.com/t/math-mavens-hopefully-easy-algebra-query/162633.md?page=2)