Complex Numbers And Quadratic Equations question 266
Question: If $ z_1,z_2,z_3……n_{n} $ are nth, roots of unity, then for $ k=1,2,…..,n $
Options:
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}}| $
Show Answer
Answer:
Correct Answer: D
Solution:
The $ {n^{th}} $ roots of unity are given by $ z_{k}={e^{\frac{i2\pi (k-1)}{n}}},(k=1,2….,n) $ \ $ |z_{k}|=| {e^{\frac{i2\pi (k-1)}{n}}} |=1 $ for all $ k=1,2,…..,n $
Þ $ |z_{k}|=|{z_{k+1}}| $ for all $ k=1,2…..,n $
BETA
