Question

The triangle formed by the complex numbers
$1,\frac{-1+i\sqrt{3}}{2},\frac{-1-i\sqrt{3}}{2}$ is

• A. equilateral
• B. right angled
• C. isosceles
• D. right angled isosceles

Answer 1

The correct option is A equilateral

the given three complex numbers are complex roots y
similarly i.e 1, $w=\left(\frac{-1+\sqrt{3}i}{2}\right)$ and $w^2=\left(\frac{-1-\sqrt{3}i}{2}\right)$
All the roots and unity lie on the unit circle with equal spacing along the circle
$\because a=b=c$ (in the diagram)
and all angles are ${60}^o$
hence it is on eqilateral $\Delta$