So, I'm guessing I should use complex numbers to find a solution for this problem. Here is the complex number which in the power of 8 equals to 4. $$\sqrt[8]{4}\left(cos\:\frac{\theta +2\pi k}{8}+isin\frac{\theta \:+2\pi \:k}{8}\right)$$ But how can I find every single one of them?
Find every number which in the power of 8 equals to 4
0
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linear-algebra
complex-numbers
1 Answers
2
$$z^{8}=4$$
$$ z^{8}=4e^{0+2\pi k}$$
$$ z=4^{\frac{1}{8}}e^{\frac{2\pi k}{8}} $$
Now let $k=0,1,2,3...7$ you will find all solutions.