Question

Omega square value omega cube value

Answer 1

Answer:

omega square is equal to one in complex numbers omega square is not equal to 1 . it's cube is equal to one .cube root of unity are 1,ω,ω^2.where 1+ω+ω^2=0,{ω=(-1+i√3)/2, so ω^2=1/ω,and finally ω^3=1.

Explanation:

Answer 2

The values of $\omega$ and $\omega^2$ are - (1 + $\omega$) or $\omega^2=\dfrac{-1-i\sqrt{3}}{2}$ and $\omega^3=1$.

Explanation:

We have,

$\omega$ and $\omega^2$

To find, the value of $\omega$ and $\omega^2$ = ?

We know that,

1, $\omega$ and $\omega^2$ cube root of unity.

∴ 1 + $\omega$ + $\omega^2$ = 0

⇒ $\omega^2$ = - (1 + $\omega$)

$\omega=\dfrac{-1+i\sqrt{3}}{2}$ and $\omega^2=\dfrac{-1-i\sqrt{3}}{2}$

$\omega^3=1$

∴ $\omega^2$ = - (1 + $\omega$) or $\omega^2=\dfrac{-1-i\sqrt{3}}{2}$ and $\omega^3=1$

Thus, the values of $\omega$ and $\omega^2$ are - (1 + $\omega$) or $\omega^2=\dfrac{-1-i\sqrt{3}}{2}$ and $\omega^3=1$.