Question

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

• A. TRUE
• B. FALSE

Answer 1

The correct option is A TRUE

We know , $1,\omega \text{and}{\omega }^2$ are cube roots of unity , plotting the vertices of the triangle on Argand plane.


$\omega =-\frac{1}{2}+\frac{i\sqrt{3}}{3},{\omega }^2=-\frac{1}{2}-\frac{i\sqrt{3}}{2}$

$|1-\omega |=|\frac{3}{2}-\frac{i\sqrt{3}}{2}|=\sqrt{3}$

$|\omega -{\omega }^2|=|i\sqrt{3}|=\sqrt{3}$

$|1-{\omega }^2|=|\frac{3}{2}+\frac{i\sqrt{3}}{2}|=\sqrt{3}$

$\Rightarrow |1-\omega |=|\omega -{\omega }^2|=|{\omega }^2-1|$

So, the triangle formed is equilateral.
Hence, the given statement is true.