Q. The centre of a regular hexagon is at the point$z = i$. If one of its vertices is at $2 + i$, then the adjacent vertices of $2 + i$ are at the points
A) $1 \pm 2i$
B) $i + 1 \pm \sqrt{3}$
C) $2 + i(1 \pm \sqrt{3})$
D) $1 + i(1 \pm \sqrt{3})$
Explanation
(d)
Given, $z = i$
Let $z_{1} = 1 + i\left( 1 \pm \sqrt{3} \right)$ and $z_{2} = 2 + i$
Now, $\left| z_{2} - z \right| = |1 + i - i| = 2$
As we know that the distance from the centre to every vertices is equal
Now, $\left| z_{1} - z \right| = |1 + i\left( 1 \pm \sqrt{3} \right) - i|$
$= |1 \pm i\sqrt{3}|$
$= \sqrt{1^{2} + \left( \sqrt{3} \right)^{2}} = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.