Aspire Faculty ID #15274 · Topic: JAMIA MCA 2016 · Just now
JAMIA MCA 2016

If $\omega$ is a cube root of unity, then the value of $(1 + \omega - \omega^{2})(1 - \omega + \omega^{2})$ is …

Solution

We know $\omega^{3} = 1$ and $1 + \omega + \omega^{2} = 0$. Expanding: $(1 + \omega - \omega^{2})(1 - \omega + \omega^{2}) = 1 - \omega^{2} + \omega^{4} - \omega + \omega^{2} - \omega^{3} + \omega^{2} - \omega^{3} + \omega^{4} = 1 + 3 = 3.$
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