Question

Let $z_1$ and $z_2$ be nth roots of unity which subtend a right angle an at the origin. Then $n$ must be of the form

• A. $4k+1$
• B. $4k+2$
• C. $4k+3$
• D. $4k$

Answer 1

The correct option is D $4k$

$arg\left(\frac{z_1}{z_2}\right)=\frac{\pi }{2}$

$\frac{z_1}{z_2}=i$

${\left(\frac{z_1}{z_2}\right)}^n=i^n=1$

$\Rightarrow n=4k$