(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find all the roots of [itex]z^{6} = -2[/itex]

2. Relevant 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]

3. 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 any one could tell me how I find [itex]\theta[/itex] that would be great.

Thanks in advance.

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# Homework Help: Complex roots and de Moivre's formula

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