Question

A regular hexagon is drawn with two of its vertices forming a shorter diagonal at z = –2 and z = 1 – i$\sqrt{3}$. The other four vertices are-

• A. ± 2$\sqrt{3}$, ± I
• B. ±$\sqrt{3}$, ± i
• C. $\sqrt{3}$, $\sqrt{3}$± i, –1–i$\sqrt{3}$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Sol. A regular hexagon is circumscribed by a circle with its centre at the centre of the hexagon and radius equal to the length of a side. The sides subtend an angle of p/3 at the centre. The length of a shorter diagonal = 2$\sqrt{3}$. Length of a side is therefore $\sqrt{3}$sec $\frac{\pi}{6}$= 2 = radius of the circle. Centre is Z = 0 and the other vertices are 2, ± 1 + i$\sqrt{3}$and –1 –i$\sqrt{3}$.