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Math Challenge III 2.20 Algebra

 
 
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Re: Math Challenge III 2.20 Algebra
by Dr. Kevin Wang - Tuesday, 7 July 2020, 1:36 AM
 

$1$ doesn't count because $\omega$ is imaginary.  The other two give you the same result.  Working with roots of unity, you don't need to convert to rectangular form.  Instead, use the fact that $\omega^3=1$, and $\omega^2+\omega+1=0$, you will find the algebra pretty easy.