0
$\begingroup$

$(2i)^{1/2}$

$(1-\sqrt{3}i)^{1/2}$

$(-1)^{1/3}$

$(-16)^{1/4}$

How can I find the roots of the complex numbers above?

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    May look into http://math.stackexchange.com/questions/201769/solving-roots-of-complex-number/201774#2017742012-10-25

2 Answers 2

2

Use de Moivre's theorem: $z^{1/n} = r^{1/n} \exp \left( i\frac{\theta + 2\pi k}{n} \right)$ for $k = 0, 1, 2, \ldots, n - 1$. The formula is not difficult to derive as we only need to write $z$ in the polar form and take the $n$th root of both sides.

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    If you still do not understand use YouTube, there must be a good explanation.2012-10-25
1

Use DeMoivre's formula.

Don't forget that cos and sin functions are $2\pi$ periodic