- #1
Jonmundsson
- 22
- 0
Homework Statement
Find all the roots of [itex]z^{6} = -2[/itex]
Homework Equations
[itex]z = \sqrt[n]{r} (cos(\frac{\theta}{n} + k\cdot \frac{2\pi}{n}) + isin(\frac{\theta}{n} + k\cdot \frac{2\pi}{n})[/itex] where [itex]k = 0, 1, \cdots, n - 1[/itex]
The Attempt at a Solution
I know that [itex]r = \sqrt{x^2 + y^2} = \sqrt{(-2)^2} = 2[/itex] but I don't understand how I find [itex]\theta[/itex]. [itex]arg z = arg -2[/itex] isn't a nice number to work with and now I'm stumped. This is the only thing holding me back since the formula is pretty straightforward so if anyone could tell me how I find [itex]\theta[/itex] that would be great.
Thanks in advance.