omega is an imaginary cube root of unity. If | vedclass

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(D) Given the equation: $(1 + \omega^2)^m = (1 + \omega^4)^m$.Since $\omega^3 = 1$,we have $\omega^4 = \omega$.Substituting this into the equation: $(

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$3$

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(D) Given the equation: $(1 + \omega^2)^m = (1 + \omega^4)^m$.Since $\omega^3 = 1$,we have $\omega^4 = \omega$.Substituting this into the equation: $(1 + \omega^2)^m = (1 + \omega)^m$.Using the property $1 + \omega + \omega^2 = 0$,we know $1 + \omega^2 = -\omega$ and $1 + \omega = -\omega^2$.So,$(-\omega)^m = (-\omega^2)^m$.Dividing both sides by $(-\omega)^m$ (assuming $\omega 
eq 0$): $1 = \frac{(-\omega^2)^m}{(-\omega)^m} = (\frac{-\omega^2}{-\omega})^m = (\omega)^m$.For $(\omega)^m = 1$,the smallest positive integer $m$ must be $3$ because $\omega^3 = 1$.

$\omega$ is an imaginary cube root of unity. If $(1 + \omega^2)^m = (1 + \omega^4)^m$,then the least positive integral value of $m$ is

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