A) \[|{{z}_{k}}|=k|{{z}_{k+1}}|\]
B) \[|{{z}_{k+1}}|=k|{{z}_{k}}|\]
C) \[|{{z}_{k+1}}|\,=\,|{{z}_{k}}|+|{{z}_{k+1}}|\]
D) \[|{{z}_{k}}|=|{{z}_{k+1}}|\]
Correct Answer: D
Solution :
The \[{{n}^{\text{th}}}\]roots of unity are given by \[{{z}_{k}}={{e}^{\frac{i2\pi (k-1)}{n}}},\,\,\,\,\,(k=1,2....,n)\] \ \[|{{z}_{k}}|\,=\,\left| \,{{e}^{\frac{i2\pi (k-1)}{n}}}\, \right|=1\]for all \[k=1,2,.....,n\] Þ \[|{{z}_{k}}|\,=\,|{{z}_{k+1}}|\]for all \[k=1,2.....,n\]
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