Question

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. $1+i(1\pm \sqrt{3})$
• E. $1-i(1\pm \sqrt{3})$

Answer 1

Answer: (D)

Given, $z=i$ Let $z_1+1+i(1\pm \sqrt{3})$ and $z_2=2+i$ Now, $|z_2-z|=|2+i-i|$
$=2$
As we know that the distance from the centre to every vertices is equal.
Now, $|z_1-z|=|1+i(1\pm \sqrt{3})-i|$
$=|1\pm i\sqrt{3}|=\sqrt{1^2+{(\sqrt{3})}^2}$
$=2$
Hence, option (d) is correct.