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Finding the n-th Roots of a Complex Number
To find the \(n\)-th roots of a complex number \(z\), we use De Moivre's Theorem. First, convert \(z\) to its polar form \(z = r(\cos\theta + i\sin\theta)\).
The \(n\) roots are given by the formula:
$$ z_k = \sqrt[n]{r} \left( \cos\frac{\theta + 2\pi k}{n} + i\sin\frac{\theta + 2\pi k}{n} \right) $$
for \(k = 0, 1, 2, \dots, n-1\).
Find the n-th roots of a complex number.
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