Question

The vertices of an equilateral triangle in the Argand plane represent the non real cube roots of unity. The area of the triangle is

• A. $\frac{3\sqrt{3}}{4}$
• B. $\frac{3\sqrt{3}}{2}$
• C. $3\sqrt{3}$
• D. none of these

Answer 1

The correct option is A $\frac{3\sqrt{3}}{4}$

Length of side will be
$|1-w|$
$=|1-\frac{-1+\sqrt{3}i}{2}|$
$=|\frac{3-\sqrt{3}i}{2}|$
$=\sqrt{3}$
$=a$
Hence
Area of triangle will be
$\frac{\sqrt{3}{a}^2}{4}$
$=\frac{\sqrt{3}.\left(3\right)}{4}$
$=\frac{3\sqrt{3}}{4}$