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Problem 431

Find all of the nth roots of 1 . That is, find the values of \(z\) which satisfy the equation $$ z^{\mathrm{n}}=1, z \neq 0 . $$

Expert verified

The nth roots of 1 can be expressed as the set: \[ z = \left\{ e^{i\frac{m\pi}{n}} \,|\, m = 0, 1, 2, ..., n-1 \right\} \]

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