If omega is a complex cube root of unity and | vedclass

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(C) We know that $1+\omega+\omega^2=0$,so $1+\omega=-\omega^2$. Substituting this into the given expression: $(1+\omega)^7 = (-\omega^2)^7$ $= (-1)^7

Vedclass · Accepted Answer

$1, 1$

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(C) We know that $1+\omega+\omega^2=0$,so $1+\omega=-\omega^2$. Substituting this into the given expression: $(1+\omega)^7 = (-\omega^2)^7$ $= (-1)^7 	imes (\omega^2)^7$ $= -1 	imes \omega^{14}$ Since $\omega^3=1$,we have $\omega^{14} = \omega^{12} 	imes \omega^2 = (\omega^3)^4 	imes \omega^2 = 1^4 	imes \omega^2 = \omega^2$. Thus,$(1+\omega)^7 = -\omega^2$. Using $1+\omega+\omega^2=0$,we have $-\omega^2 = 1+\omega$. Comparing $1+\omega$ with $A+B\omega$,we get $A=1$ and $B=1$.

If $\omega$ is a complex cube root of unity and $(1+\omega)^7=A+B \omega$,then the values of $A$ and $B$ are,respectively.

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