Finding the roots of complex numbers
By Emma Valentine •
$(2i)^{1/2}$
$(1-\sqrt{3}i)^{1/2}$
$(-1)^{1/3}$
$(-16)^{1/4}$
How can I find the roots of the complex numbers above?
$\endgroup$ 12 Answers
$\begingroup$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.
$\endgroup$ 4 $\begingroup$Use DeMoivre's formula.
Don't forget that cos and sin functions are $2\pi$ periodic
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