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  4. The cube roots of unity when represented on Argand diagram form the vertices of an equilateral triangle.

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Q. The cube roots of unity when represented on Argand diagram form the vertices of an equilateral triangle.

IIT JEEIIT JEE 1988Complex Numbers and Quadratic Equations

Solution:

Since, cube root of unity are $1, \omega,\omega^2$ given by
$A(1,0),B\bigg(-\frac{1}{2},-\frac{\sqrt 3}{2}\bigg), C \bigg(-\frac{1}{2},-\frac{\sqrt 3}{2}\bigg)$
$\Rightarrow AB = BC = CA = \sqrt 3$
Hence, cube roots of unity form an equilateral triangle.