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Properties of nth Root of a Complex Number

If z1, z2, z3...

Question

If $z_{1}, z_{2}, z_{3} . . . . . n_{n}$ are n^th, roots of unity, then for k = 1, 2, ....., n

A

| z_{k} | = k | z_{k + 1} |

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B

| z_{k + 1} | = k | z_{k} |

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C

| z_{k + 1} | = | z_{k} | + | z_{k + 1} |

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D

| z_{k} | = | z_{k + 1} |

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Solution

The correct option is D $| z_{k} | = | z_{k + 1} |$
The $n^{t h}$ roots of unity are given by $z_{k} = e^{\frac{i 2 π (k - 1)}{n}}, (k = 1, 2, . . . . ., n)$

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