Question

If $z_1,z_2,z_3.....n_n$ are n^th, roots of unity, then for k = 1, 2, ....., n

• A. $|z_k|=k|z_{k+1}|$
• B. $|z_{k+1}|=k|z_k|$
• C. $|z_{k+1}|=|z_k|+|z_{k+1}|$
• D. $|z_k|=|z_{k+1}|$

Answer 1

The correct option is D $|z_k|=|z_{k+1}|$

Given $z_1,z_2,z_3.....n_n$ are nth, roots of unity.
So, $|z_1|=|z_2|=|z_3|=.......=|z_n|=1$
In general $|z_k|=|z_{k+1}|=1$ for any positive integers k.