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

Question

The cube roots of unity when represented on Argand diagram form the vertices of an equilateral triangle. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Since, cube root of unity are 1, ω,ω2 given by A(1,0),B(-(1/2),-(√ 3/2)), C (-(1/2),-(√ 3/2)) ⇒ AB = BC = CA = √ 3 Hence, cube roots of unity form an equilateral triangle.

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

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

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

Since, cube root of unity are 1,ω,ω2 given by A(1,0),B(−21​,−23​​),C(−21​,−23​​) ⇒AB=BC=CA=3​ Hence, cube roots of unity form an equilateral triangle.

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