Question

The cube roots of unity when represented on the Argand plane form the vertices of an

• A. equilateral triangle
• B. isosceles triangle
• C. right angled triangle
• D. none of these

Answer 1

Answer: (A)

equilateral triangle

The cube roots of unity are represented by the vertices of a triangle.
$A=1$,$B=\omega =\left(\frac{-1}{2}+\frac{\sqrt{3}}{2}i\right)$ and
$C={\omega }^2=\left(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\right)$
$AB=\left|\frac{3}{2}-\frac{\sqrt{3}}{2}i\right|=\sqrt{3}$
$BC=\left|\frac{3}{2}+\frac{\sqrt{3}}{2}i\right|=\sqrt{3}$ and
$AC=|0+\sqrt{3}i|=\sqrt{3}$
All sides are equal.Hence, triangle is equilateral.
Hence, option A.